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Commit 2020-11-11 13:39 e1560a31

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feat(measure_theory/borel_space): continuity set of a function is measurable (#4967)

  • Move the definition of is_Gδ and basic lemmas to a separate file.
  • Prove that {x | continuous_at f x} is a Gδ set provided that the codomain is a uniform space with countable basis of the uniformity filter (e.g., an emetric_space). In particular, this set is measurable.
  • Rename nhds_le_uniformity to supr_nhds_le_uniformity.
  • Add new nhds_le_uniformity without in the statement.
  • Add uniform.continuous_at_iff_prod.

Estimated changes

added theorem is_Gδ.inter
added theorem is_Gδ.union
added def is_Gδ
added theorem is_Gδ_Inter
added theorem is_Gδ_Inter_of_open
added theorem is_Gδ_bInter
added theorem is_Gδ_bInter_of_open
added theorem is_Gδ_sInter
added theorem is_Gδ_univ
added theorem is_open.is_Gδ
added def residual
deleted theorem is_Gδ.inter
deleted theorem is_Gδ.union
deleted def is_Gδ
deleted theorem is_Gδ_Inter
deleted theorem is_Gδ_Inter_of_open
deleted theorem is_Gδ_bInter
deleted theorem is_Gδ_bInter_of_open
deleted theorem is_Gδ_sInter
deleted theorem is_Gδ_univ
deleted theorem is_open.is_Gδ
deleted def residual