[Merged by Bors] - feat: construct Haar measure in locally compact non-Hausdorff groups #9746
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Co-authored-by: Rémy Degenne <remydegenne@gmail.com>
…nity/mathlib4 into SG_haar_unique2
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…9746) The construction we have is given in T2 spaces, but it works in non-Hausdorff spaces modulo a few modifications. For this, we introduce an ad hoc class `T2OrLocallyCompactRegularSpace`, which is just enough to unify the arguments, as a replacement for the class `ClosableCompactSubsetOpenSpace` (which is not strong enough). In the file `Separation.lean`, we move some material that was only available on T2 spaces to this new class. The construction is needed for a forthcoming improvement of uniqueness results for Haar measures, based on https://mathoverflow.net/questions/456670/uniqueness-of-left-invariant-borel-probability-measure-on-compact-groups.
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The construction we have is given in T2 spaces, but it works in non-Hausdorff spaces modulo a few modifications.
For this, we introduce an ad hoc class
T2OrLocallyCompactRegularSpace, which is just enough to unify the arguments, as a replacement for the classClosableCompactSubsetOpenSpace(which is not strong enough). In the fileSeparation.lean, we move some material that was only available on T2 spaces to this new class.The construction is needed for a forthcoming improvement of uniqueness results for Haar measures, based on https://mathoverflow.net/questions/456670/uniqueness-of-left-invariant-borel-probability-measure-on-compact-groups.