[Merged by Bors] - feat(MeasureTheory): add CountablySeparated #12433
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Co-authored-by: Rémy Degenne <remydegenne@gmail.com>
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add a typeclass `CountablySeparated _` abbreviating `HasCountableSeparatingOn _ MeasurableSet univ`. This is a common assumption is measure theory and is already used often in the library. Additionally, mathlib was previously not consistent in choosing between the equivalent spellings `HasCountableSeparatingOn X MeasurableSet s` and `HasCountableSeparatingOn s MeasurableSet univ` for X a measurable space and `s : Set X`. (In the latter spelling, `s` is being coerced to the subtype of `X`.) Lemmas and instances are added to help unify the situation. This is now spelled `CountablySeparated s`. Co-authored-by: Felix-Weilacher <112423742+Felix-Weilacher@users.noreply.github.com>
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add a typeclass `CountablySeparated _` abbreviating `HasCountableSeparatingOn _ MeasurableSet univ`. This is a common assumption is measure theory and is already used often in the library. Additionally, mathlib was previously not consistent in choosing between the equivalent spellings `HasCountableSeparatingOn X MeasurableSet s` and `HasCountableSeparatingOn s MeasurableSet univ` for X a measurable space and `s : Set X`. (In the latter spelling, `s` is being coerced to the subtype of `X`.) Lemmas and instances are added to help unify the situation. This is now spelled `CountablySeparated s`. Co-authored-by: Felix-Weilacher <112423742+Felix-Weilacher@users.noreply.github.com>
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add a typeclass `CountablySeparated _` abbreviating `HasCountableSeparatingOn _ MeasurableSet univ`. This is a common assumption is measure theory and is already used often in the library. Additionally, mathlib was previously not consistent in choosing between the equivalent spellings `HasCountableSeparatingOn X MeasurableSet s` and `HasCountableSeparatingOn s MeasurableSet univ` for X a measurable space and `s : Set X`. (In the latter spelling, `s` is being coerced to the subtype of `X`.) Lemmas and instances are added to help unify the situation. This is now spelled `CountablySeparated s`. Co-authored-by: Felix-Weilacher <112423742+Felix-Weilacher@users.noreply.github.com>
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add a typeclass
CountablySeparated _abbreviatingHasCountableSeparatingOn _ MeasurableSet univ. This is a common assumption is measure theory and is already used often in the library.Additionally, mathlib was previously not consistent in choosing between the equivalent spellings
HasCountableSeparatingOn X MeasurableSet sandHasCountableSeparatingOn s MeasurableSet univfor X a measurable space ands : Set X. (In the latter spelling,sis being coerced to the subtype ofX.) Lemmas and instances are added to help unify the situation. This is now spelledCountablySeparated s.