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Commit 2021-03-28 12:00 0e4760b3

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refactor(measure_theory): add typeclasses for measurability of operations (#6832) With these typeclasses and lemmas we can use, e.g., measurable.mul for any type with measurable uncurry (*), not only those with has_continuous_mul. New typeclasses:

  • has_measurable_add, has_measurable_add₂: measurable left/right addition and measurable uncurry (+);
  • has_measurable_mul, has_measurable_mul₂: measurable left/right multiplication and measurable uncurry (*);
  • has_measurable_pow: measurable uncurry (^)
  • has_measurable_sub, has_measurable_sub₂: measurable left/right subtraction and measurable λ (a, b), a - b
  • has_measurable_div, has_measurable_div₂ : measurability of division as a function of numerator/denominator and measurability of λ (a, b), a / b;
  • has_measurable_neg, has_measurable_inv: measurable negation/inverse;
  • has_measurable_const_smul, has_measurable_smul: measurable λ x, c • x and measurable λ (c, x), c • x

Estimated changes

added theorem ae_measurable.div
added theorem ae_measurable.inv
added theorem ae_measurable.mul
added theorem ae_measurable.pow
added theorem ae_measurable.smul
added theorem ae_measurable_inv_iff'
added theorem ae_measurable_inv_iff
added theorem finset.measurable_prod
added theorem list.measurable_prod'
added theorem list.measurable_prod
added theorem measurable.const_div
added theorem measurable.const_mul
added theorem measurable.const_pow
added theorem measurable.const_smul'
added theorem measurable.const_smul
added theorem measurable.div
added theorem measurable.div_const
added theorem measurable.inv
added theorem measurable.mul
added theorem measurable.mul_const
added theorem measurable.pow
added theorem measurable.pow_const
added theorem measurable.smul
added theorem measurable.smul_const
added theorem measurable_inv_iff'
added theorem measurable_inv_iff
deleted theorem ae_measurable.const_smul
deleted theorem ae_measurable.ennreal_mul
deleted theorem ae_measurable.inv
deleted theorem ae_measurable.mul
deleted theorem ae_measurable.pow
deleted theorem ae_measurable.smul
deleted theorem ae_measurable.sub
deleted theorem ennreal.measurable_div
deleted theorem ennreal.measurable_inv
deleted theorem ennreal.measurable_mul
deleted theorem ennreal.measurable_sub
deleted theorem finset.ae_measurable_prod
deleted theorem finset.measurable_prod
deleted theorem measurable.const_mul
deleted theorem measurable.const_smul
deleted theorem measurable.div
deleted theorem measurable.ennreal_div
deleted theorem measurable.ennreal_inv
deleted theorem measurable.ennreal_mul
deleted theorem measurable.ennreal_sub
deleted theorem measurable.inv'
deleted theorem measurable.inv
deleted theorem measurable.mul'
deleted theorem measurable.mul
deleted theorem measurable.mul_const
deleted theorem measurable.of_inv
deleted theorem measurable.pow
deleted theorem measurable.smul
deleted theorem measurable.sub
deleted theorem measurable.sub_const
deleted theorem measurable.sub_nnreal
deleted theorem measurable_const_smul_iff
deleted theorem measurable_inv'
deleted theorem measurable_inv
deleted theorem measurable_inv_iff
deleted theorem measurable_mul
deleted theorem measurable_mul_left
deleted theorem measurable_mul_right
deleted theorem measurable_pow