Mathlib Changelog
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2018-07-19 15:34
29639b31
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feat(analysis/measure_theory): optimize proofs; trim, is_complete
Estimated changes
Modified
algebra/ordered_field.lean
added
theorem
one_half_lt_one
added
theorem
one_half_pos
Modified
analysis/ennreal.lean
added
theorem
ennreal.add_left_inj
added
theorem
ennreal.add_right_inj
added
theorem
ennreal.add_sub_self'
added
theorem
ennreal.add_supr
added
theorem
ennreal.exists_pos_sum_of_encodable
added
theorem
ennreal.of_real_add_le
added
theorem
ennreal.sub_infi
added
theorem
ennreal.sub_le_self
added
theorem
ennreal.sub_sub_cancel
modified
theorem
ennreal.sub_supr
added
theorem
ennreal.supr_add_supr
Modified
analysis/limits.lean
added
theorem
is_sum_geometric_two
added
def
pos_sum_of_encodable
Modified
analysis/measure_theory/borel_space.lean
added
def
measure_theory.borel
deleted
theorem
measure_theory.borel_eq_generate_from_Iio_rat
deleted
theorem
measure_theory.borel_eq_generate_from_Ioo_rat
added
theorem
measure_theory.borel_prod_le
deleted
theorem
measure_theory.is_topological_basis_Ioo_rat
added
theorem
real.borel_eq_generate_from_Iio_rat
added
theorem
real.borel_eq_generate_from_Ioo_rat
Modified
analysis/measure_theory/lebesgue_measure.lean
added
theorem
measure_theory.is_lebesgue_measurable_Iio
deleted
theorem
measure_theory.le_lebesgue_length
modified
def
measure_theory.lebesgue
added
theorem
measure_theory.lebesgue_Icc
modified
def
measure_theory.lebesgue_length
added
theorem
measure_theory.lebesgue_length_Icc
deleted
theorem
measure_theory.lebesgue_length_Ico'
modified
theorem
measure_theory.lebesgue_length_Ico
added
theorem
measure_theory.lebesgue_length_Ioo
added
theorem
measure_theory.lebesgue_length_eq_infi_Icc
added
theorem
measure_theory.lebesgue_length_eq_infi_Ioo
added
theorem
measure_theory.lebesgue_length_mono
added
theorem
measure_theory.lebesgue_outer_Icc
modified
theorem
measure_theory.lebesgue_outer_Ico
added
theorem
measure_theory.lebesgue_outer_Ioo
deleted
theorem
measure_theory.lebesgue_outer_is_measurable_Iio
added
theorem
measure_theory.lebesgue_outer_le_length
added
theorem
measure_theory.lebesgue_outer_singleton
added
theorem
measure_theory.lebesgue_outer_trim
modified
theorem
measure_theory.lebesgue_singleton
added
theorem
measure_theory.lebesgue_to_outer_measure
added
theorem
measure_theory.lebesgue_val
deleted
theorem
measure_theory.tendsto_of_nat_at_top_at_top
Modified
analysis/measure_theory/measurable_space.lean
added
theorem
encodable.Union_decode2
added
theorem
encodable.Union_decode2_cases
added
theorem
is_measurable.Inter
added
theorem
is_measurable.Union
added
theorem
is_measurable.bInter
added
theorem
is_measurable.bUnion
added
theorem
is_measurable.compl
added
theorem
is_measurable.compl_iff
added
theorem
is_measurable.diff
added
theorem
is_measurable.disjointed
added
theorem
is_measurable.empty
added
theorem
is_measurable.inter
added
theorem
is_measurable.sInter
added
theorem
is_measurable.sUnion
added
theorem
is_measurable.sub
added
theorem
is_measurable.union
modified
def
is_measurable
deleted
theorem
is_measurable_Inter
deleted
theorem
is_measurable_Union
deleted
theorem
is_measurable_Union_nat
deleted
theorem
is_measurable_bInter
deleted
theorem
is_measurable_bUnion
deleted
theorem
is_measurable_compl
deleted
theorem
is_measurable_disjointed
deleted
theorem
is_measurable_empty
deleted
theorem
is_measurable_inter
deleted
theorem
is_measurable_sInter
deleted
theorem
is_measurable_sUnion
deleted
theorem
is_measurable_sdiff
deleted
theorem
is_measurable_sub
deleted
theorem
is_measurable_union
added
theorem
measurable.comp
added
theorem
measurable.if
added
theorem
measurable.preimage
added
theorem
measurable.prod
deleted
theorem
measurable_comp
deleted
theorem
measurable_if
deleted
theorem
measurable_prod
added
theorem
measurable_space.Union_decode2_disjoint_on
deleted
theorem
measurable_space.dynkin_system.dynkin_system_eq
added
theorem
measurable_space.dynkin_system.ext
modified
theorem
measurable_space.dynkin_system.generate_le
added
theorem
measurable_space.dynkin_system.has_Union
added
theorem
measurable_space.dynkin_system.has_compl_iff
added
theorem
measurable_space.dynkin_system.has_diff
deleted
theorem
measurable_space.dynkin_system.has_sdiff
modified
theorem
measurable_space.dynkin_system.has_union
modified
def
measurable_space.dynkin_system.restrict_on
added
theorem
measurable_space.ext
added
theorem
measurable_space.is_measurable_Inf
added
theorem
measurable_space.is_measurable_inf
added
theorem
measurable_space.is_measurable_infi
deleted
theorem
measurable_space_eq
Modified
analysis/measure_theory/measure_space.lean
added
def
completion
added
theorem
is_measurable.diff_null
added
theorem
is_measurable.is_null_measurable
added
theorem
is_null_measurable.Union_nat
added
theorem
is_null_measurable.compl
added
theorem
is_null_measurable.diff_null
added
theorem
is_null_measurable.union_null
added
def
is_null_measurable
added
theorem
is_null_measurable_iff
added
theorem
is_null_measurable_measure_eq
added
theorem
is_null_measurable_of_complete
modified
theorem
measure_theory.le_to_outer_measure_caratheodory
added
def
measure_theory.measure'
added
theorem
measure_theory.measure'_Union
added
theorem
measure_theory.measure'_Union_le_tsum_nat'
added
theorem
measure_theory.measure'_Union_le_tsum_nat
added
theorem
measure_theory.measure'_Union_nat
added
theorem
measure_theory.measure'_empty
added
theorem
measure_theory.measure'_eq
added
theorem
measure_theory.measure'_mono
added
theorem
measure_theory.measure'_union
added
theorem
measure_theory.measure.add_apply
added
theorem
measure_theory.measure.add_to_outer_measure
added
def
measure_theory.measure.count
added
def
measure_theory.measure.dirac
added
theorem
measure_theory.measure.dirac_apply
added
theorem
measure_theory.measure.ext
added
def
measure_theory.measure.is_complete
added
theorem
measure_theory.measure.le_iff'
added
theorem
measure_theory.measure.le_iff
added
def
measure_theory.measure.map
added
theorem
measure_theory.measure.map_apply
added
theorem
measure_theory.measure.map_id
added
theorem
measure_theory.measure.map_map
added
def
measure_theory.measure.of_measurable
added
def
measure_theory.measure.sum
added
theorem
measure_theory.measure.to_outer_measure_le
added
theorem
measure_theory.measure.zero_apply
added
theorem
measure_theory.measure.zero_to_outer_measure
added
structure
measure_theory.measure
added
theorem
measure_theory.measure_Union
added
theorem
measure_theory.measure_Union_le
deleted
theorem
measure_theory.measure_Union_le_tsum_nat
deleted
theorem
measure_theory.measure_Union_nat
added
theorem
measure_theory.measure_Union_null
modified
theorem
measure_theory.measure_bUnion
added
theorem
measure_theory.measure_diff
modified
theorem
measure_theory.measure_empty
added
theorem
measure_theory.measure_eq_infi
added
theorem
measure_theory.measure_eq_measure'
added
theorem
measure_theory.measure_eq_outer_measure'
added
theorem
measure_theory.measure_eq_trim
modified
theorem
measure_theory.measure_mono
added
theorem
measure_theory.measure_mono_null
modified
theorem
measure_theory.measure_sUnion
deleted
theorem
measure_theory.measure_sdiff
deleted
def
measure_theory.measure_space.count
deleted
def
measure_theory.measure_space.dirac
deleted
def
measure_theory.measure_space.map
deleted
theorem
measure_theory.measure_space.map_comp
deleted
theorem
measure_theory.measure_space.map_id
deleted
theorem
measure_theory.measure_space.map_measure
deleted
def
measure_theory.measure_space.sum
deleted
structure
measure_theory.measure_space
deleted
theorem
measure_theory.measure_space_eq
deleted
theorem
measure_theory.measure_space_eq_of
added
theorem
measure_theory.measure_union_le
added
theorem
measure_theory.measure_union_null
added
def
measure_theory.outer_measure'
added
theorem
measure_theory.outer_measure'_eq
added
theorem
measure_theory.outer_measure'_eq_measure'
added
theorem
measure_theory.outer_measure.le_trim_iff
modified
def
measure_theory.outer_measure.to_measure
added
def
measure_theory.outer_measure.trim
added
theorem
measure_theory.outer_measure.trim_add
added
theorem
measure_theory.outer_measure.trim_congr
added
theorem
measure_theory.outer_measure.trim_eq
added
theorem
measure_theory.outer_measure.trim_eq_infi'
added
theorem
measure_theory.outer_measure.trim_eq_infi
added
theorem
measure_theory.outer_measure.trim_ge
added
theorem
measure_theory.outer_measure.trim_le_trim
added
theorem
measure_theory.outer_measure.trim_sum_ge
added
theorem
measure_theory.outer_measure.trim_trim
added
theorem
measure_theory.outer_measure.trim_zero
added
theorem
measure_theory.to_measure_apply
added
theorem
measure_theory.to_measure_to_outer_measure
added
theorem
measure_theory.to_outer_measure_apply
added
theorem
measure_theory.to_outer_measure_eq_outer_measure'
modified
theorem
measure_theory.to_outer_measure_to_measure
added
theorem
null_is_null_measurable
added
def
null_measurable
Modified
analysis/measure_theory/outer_measure.lean
added
theorem
measure_theory.outer_measure.Sup_apply
added
theorem
measure_theory.outer_measure.Union_aux
added
theorem
measure_theory.outer_measure.Union_null
added
theorem
measure_theory.outer_measure.add_apply
added
theorem
measure_theory.outer_measure.add_smul
deleted
theorem
measure_theory.outer_measure.caratheodory_is_measurable_eq
added
def
measure_theory.outer_measure.dirac
added
theorem
measure_theory.outer_measure.dirac_apply
added
theorem
measure_theory.outer_measure.dirac_caratheodory
added
theorem
measure_theory.outer_measure.empty'
added
theorem
measure_theory.outer_measure.ext
added
theorem
measure_theory.outer_measure.is_caratheodory
added
theorem
measure_theory.outer_measure.is_caratheodory_le
added
theorem
measure_theory.outer_measure.le_add_caratheodory
added
theorem
measure_theory.outer_measure.le_of_function
added
theorem
measure_theory.outer_measure.le_smul_caratheodory
added
theorem
measure_theory.outer_measure.le_sum_caratheodory
added
def
measure_theory.outer_measure.map
added
theorem
measure_theory.outer_measure.map_apply
added
theorem
measure_theory.outer_measure.map_id
added
theorem
measure_theory.outer_measure.map_map
added
theorem
measure_theory.outer_measure.mono'
added
theorem
measure_theory.outer_measure.mul_smul
added
theorem
measure_theory.outer_measure.one_smul
deleted
theorem
measure_theory.outer_measure.outer_measure_eq
added
def
measure_theory.outer_measure.smul
added
theorem
measure_theory.outer_measure.smul_add
added
theorem
measure_theory.outer_measure.smul_apply
added
theorem
measure_theory.outer_measure.smul_dirac_apply
added
theorem
measure_theory.outer_measure.smul_zero
deleted
theorem
measure_theory.outer_measure.subadditive
added
def
measure_theory.outer_measure.sum
added
theorem
measure_theory.outer_measure.sum_apply
added
theorem
measure_theory.outer_measure.sup_apply
added
theorem
measure_theory.outer_measure.supr_apply
added
theorem
measure_theory.outer_measure.top_apply
added
theorem
measure_theory.outer_measure.union_null
added
theorem
measure_theory.outer_measure.zero_apply
added
theorem
measure_theory.outer_measure.zero_caratheodory
added
theorem
measure_theory.outer_measure.zero_smul
Modified
analysis/real.lean
added
theorem
compact_Icc
deleted
theorem
compact_ivl
modified
theorem
rat.totally_bounded_Icc
added
theorem
real.is_topological_basis_Ioo_rat
modified
theorem
real.totally_bounded_Icc
added
theorem
tendsto_of_nat_at_top_at_top
Modified
analysis/topology/infinite_sum.lean
modified
theorem
has_sum_mul_left
modified
theorem
has_sum_mul_right
modified
theorem
is_sum_mul_left
modified
theorem
is_sum_mul_right
added
theorem
tsum_equiv
added
theorem
tsum_fintype
modified
theorem
tsum_mul_left
modified
theorem
tsum_mul_right
Modified
analysis/topology/topological_space.lean
added
theorem
topological_space.is_open_sUnion_countable
Modified
analysis/topology/topological_structures.lean
modified
theorem
closure_le_eq
added
theorem
is_closed_Icc
Modified
data/set/basic.lean
modified
theorem
set.mem_diff
deleted
theorem
set.mem_diff_eq
deleted
theorem
set.mem_diff_iff
added
theorem
set.mem_diff_of_mem
added
theorem
set.union_diff_distrib
Modified
data/set/countable.lean
Modified
data/set/disjointed.lean
added
theorem
pairwise_disjoint_on_bool
added
theorem
pairwise_on_bool
added
theorem
set.Inter_lt_succ
added
theorem
set.Union_disjointed
added
theorem
set.Union_disjointed_of_mono
added
theorem
set.Union_lt_succ
deleted
theorem
set.disjointed_Union
Modified
data/set/intervals.lean
added
def
set.Icc
added
theorem
set.Icc_diff_Ico_eq_singleton
added
theorem
set.Icc_eq_empty
added
theorem
set.Icc_eq_empty_iff
added
theorem
set.Icc_self
added
theorem
set.Icc_subset_Icc
added
theorem
set.Icc_subset_Icc_left
added
theorem
set.Icc_subset_Icc_right
added
theorem
set.Icc_subset_Ico_right
added
theorem
set.Ico_diff_Iio
added
theorem
set.Ico_diff_Ioo_eq_singleton
modified
theorem
set.Ico_eq_Ico_iff
modified
theorem
set.Ico_eq_empty
modified
theorem
set.Ico_eq_empty_iff
added
theorem
set.Ico_inter_Iio
deleted
theorem
set.Ico_inter_Iio_eq
deleted
theorem
set.Ico_sdiff_Iio_eq
deleted
theorem
set.Ico_sdiff_Ioo_eq_singleton
modified
theorem
set.Ico_self
added
theorem
set.Ico_subset_Icc_self
added
theorem
set.Ico_subset_Ico
modified
theorem
set.Ico_subset_Ico_iff
modified
theorem
set.Ico_subset_Ico_left
modified
theorem
set.Ico_subset_Ico_right
modified
theorem
set.Ico_subset_Iio_self
added
theorem
set.Iio_ne_empty
added
theorem
set.Ioo_eq_empty
added
theorem
set.Ioo_eq_empty_iff
deleted
theorem
set.Ioo_eq_empty_of_ge
modified
theorem
set.Ioo_self
added
theorem
set.Ioo_subset_Icc_self
modified
theorem
set.Ioo_subset_Ico_self
added
theorem
set.Ioo_subset_Ioo
added
theorem
set.Ioo_subset_Ioo_iff
added
theorem
set.Ioo_subset_Ioo_left
added
theorem
set.Ioo_subset_Ioo_right
added
theorem
set.mem_Icc
added
theorem
set.mem_Ico
added
theorem
set.mem_Iio
added
theorem
set.mem_Ioo
Modified
order/complete_lattice.lean
modified
theorem
lattice.infi_and
modified
theorem
lattice.infi_prod
modified
theorem
lattice.infi_sigma
modified
theorem
lattice.infi_subtype
modified
theorem
lattice.supr_and
modified
theorem
lattice.supr_prod
modified
theorem
lattice.supr_sigma
modified
theorem
lattice.supr_subtype