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• CommentRowNumber1.
• CommentAuthorTobyBartels
• CommentTimeOct 3rd 2011

I wrote about Dmitri Pavlov’s concept of measurable locales.

• CommentRowNumber2.
• CommentAuthorMike Shulman
• CommentTimeOct 3rd 2011

Very interesting, thanks!

• CommentRowNumber3.
• CommentAuthorTobyBartels
• CommentTimeOct 3rd 2011

(That should be measurable locale to avoid the cache bug.)

• CommentRowNumber4.
• CommentAuthorDmitri Pavlov
• CommentTimeOct 24th 2012
I fixed the section about Lebesgue measurable sets, which used to claim that topological manifolds have enough structure to talk about measure 0 sets.
This is not true, because there are homeomorphisms of R that send a measure 0 set in R to a set whose complement has measure 0.
Thus we need smooth manifolds and submersions instead of topological manifolds and surjections.
[I wonder if this could be done for PL manifolds...]
• CommentRowNumber5.
• CommentAuthorTobyBartels
• CommentTimeOct 25th 2012

I’m just glad that this is the only thing that you had to correct!

• CommentRowNumber6.
• CommentAuthorspitters
• CommentTimeSep 6th 2016

Added a reference to Simpson’s work on sigma-locales. There is no full theory yet, but the ideas are related.

• CommentRowNumber7.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 15th 2020

The paper https://arxiv.org/abs/2005.05284 discusses the Gelfand-type duality between commutative von Neumann algebras, measurable locales, hyperstonean locales, hyperstonean spaces, and compact strictly localizable enhanced measurable spaces.

In particular, it introduces and studies some elementary properties of the category of measurable locales.

• CommentRowNumber8.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 15th 2020

@Toby Bartels: Can we rename this thread to “measurable locale” so that the software will deposit future edits here?

• CommentRowNumber9.
• CommentAuthorTodd_Trimble
• CommentTimeMay 15th 2020
• (edited May 15th 2020)

(never mind)

• CommentRowNumber10.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 17th 2020

Minor corrections, some statements strengthened.

1. I have changed the thread title now and merged it with #10.

• CommentRowNumber12.
• CommentAuthorDmitri Pavlov
• CommentTimeMay 20th 2020

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