[Merged by Bors] - feat(measure_theory/borel_space): continuity set of a function is measurable #4967
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…surable
* 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`.
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sgouezel
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Nov 11, 2020
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…surable (#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`. Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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is_Gδand basic lemmas to a separate file.{x | continuous_at f x}is a Gδ set provided that thecodomain is a uniform space with countable basis of the uniformity
filter (e.g., an
emetric_space). In particular, this set ismeasurable.
nhds_le_uniformitytosupr_nhds_le_uniformity.nhds_le_uniformitywithout⨆in the statement.uniform.continuous_at_iff_prod.