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nLab > Latest Changes: measurable locale

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  1.  
    • 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 16th 2020
    • (edited May 16th 2020)

    (never mind)

    • CommentRowNumber10.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 17th 2020

    Minor corrections, some statements strengthened.

    diff, v21, current

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

    • CommentRowNumber12.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 21st 2020

    Added a link to my own paper, hopefully not too self-promotional.

    diff, v22, current

  13. The category theory zulip thinks that the paragraph about the sigma-locale approach to measure theory in the Constructive mathematics section should be removed:

    https://categorytheory.zulipchat.com/#narrow/stream/229136-theory.3A-category-theory/topic/One.20universe.20as.20a.20foundation.20.26.20friends/near/466112440

    There is no actual constructive measure theory using sigma-locales, and plenty of debate on whether sigma-locales are a good approach to measure theory in general.

    Thomas van Kooten

    diff, v26, current

  14. Moved the section titled “Related work” in measurable locale about the sigma-locale approach to the measure theory article

    Thomas van Kooten

    diff, v26, current

    • CommentRowNumber15.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 30th 2024

    @Thomas: the syntax for making a raw url a link is <https://example.com>, and should work in the edit box

    https://categorytheory.zulipchat.com/#narrow/stream/229136-theory.3A-category-theory/topic/One.20universe.20as.20a.20foundation.20.26.20friends/near/466112440

1 to 15 of 15

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