Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundle bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory infinity integration integration-theory itex k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics planar pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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.

    diff, v21, current

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

    • CommentRowNumber12.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 20th 2020

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

    diff, v22, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)