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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical 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 foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck 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 homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics 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 sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 2nd 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded publication data to: * [[Simon Henry]], _Measure theory over boolean toposes_, Mathematical Proceedings of the Cambridge Philosophical Society Volume 163 Issue 1, 2016 ([arXiv:1411.1605](https://arxiv.org/abs/1411.1605), [doi:10.1017/S0305004116000700](https://doi.org/10.1017/S0305004116000700)) <a href="https://ncatlab.org/nlab/revision/diff/measure+theory/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/measure+theory/11">v11</a>, <a href="https://ncatlab.org/nlab/show/measure+theory">current</a>

   added publication data to:

   • Simon Henry, Measure theory over boolean toposes, Mathematical Proceedings of the Cambridge Philosophical Society Volume 163 Issue 1, 2016 (arXiv:1411.1605, doi:10.1017/S0305004116000700)

   diff, v11, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 2nd 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to * Matthew Jackson, _A sheaf-theoretic approach to measure theory_, 2006. ([pdf](http://www.andrew.cmu.edu/~awodey/students/jackson.pdf), [d-scholarship:7348](http://d-scholarship.pitt.edu/7348)) <a href="https://ncatlab.org/nlab/revision/diff/measure+theory/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/measure+theory/11">v11</a>, <a href="https://ncatlab.org/nlab/show/measure+theory">current</a>

   added pointer to

   • Matthew Jackson, A sheaf-theoretic approach to measure theory, 2006. (pdf, d-scholarship:7348)

   diff, v11, current

3. • CommentRowNumber3.
   • CommentAuthorDmitri Pavlov
   • CommentTimeMar 19th 2021
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded references: A comprehensive five-volume treatise (with a sixth volume forthcoming) is * [[David H. Fremlin]], _[[Measure Theory]]_, Volumes 1–5, Torres Fremlin, Colchester. Volume 1, 2000; Volume 2, 2001; Volume 3, 2002; Volume 4, 2003; Volume 5, 2008. [Website](https://www1.essex.ac.uk/maths/people/fremlin/mt.htm). A more concise two-volume treatise is * [[Vladimir Bogachev]], _[[Measure theory]]_, Volumes I, II. Springer, 2007. ISBN: 978-3-540-34513-8, 3-540-34513-2. A classical (slightly dated) concise treatise is * [[Paul Halmos]], _Measure Theory_, D. Van Nostrand Company, 1950. * [[Donald L. Cohn]], _Measure Theory_, Birkhäuser, 1980. ISBN: 3-7643-3003-1 <a href="https://ncatlab.org/nlab/revision/diff/measure+theory/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/measure+theory/12">v12</a>, <a href="https://ncatlab.org/nlab/show/measure+theory">current</a>

   Added references:

   A comprehensive five-volume treatise (with a sixth volume forthcoming) is

   • David H. Fremlin, Measure Theory, Volumes 1–5, Torres Fremlin, Colchester. Volume 1, 2000; Volume 2, 2001; Volume 3, 2002; Volume 4, 2003; Volume 5, 2008. Website.

   A more concise two-volume treatise is

   • Vladimir Bogachev, Measure theory, Volumes I, II. Springer, 2007. ISBN: 978-3-540-34513-8, 3-540-34513-2.

   A classical (slightly dated) concise treatise is

   • Paul Halmos, Measure Theory, D. Van Nostrand Company, 1950.

   • Donald L. Cohn, Measure Theory, Birkhäuser, 1980. ISBN: 3-7643-3003-1

   diff, v12, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 28th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Asgar Jamneshan]], [[Terence Tao]], _Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration_ ([arXiv:2010.00681](arXiv:2010.00681)) (thanks to David's comment [here](https://nforum.ncatlab.org/discussion/5833/measure-theory-and-boolean-toposes/?Focus=94202#Comment_94202)) and am copying this also to *[[Boolean topos]]* <a href="https://ncatlab.org/nlab/revision/diff/measure+theory/14">diff</a>, <a href="https://ncatlab.org/nlab/revision/measure+theory/14">v14</a>, <a href="https://ncatlab.org/nlab/show/measure+theory">current</a>

   added pointer to:

   • Asgar Jamneshan, Terence Tao, Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical disintegration (arXiv:2010.00681)

   (thanks to David’s comment here)

   and am copying this also to Boolean topos

   diff, v14, current

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 28th 2021
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThe original [post by Tao](https://terrytao.wordpress.com/2014/07/15/real-analysis-relative-to-a-finite-measure-space/) seems to chime with your 'random as reader monad' [idea](https://nforum.ncatlab.org/discussion/6352/necessity-and-possibility/?Focus=52974#Comment_52974).

   The original post by Tao seems to chime with your ’random as reader monad’ idea.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJul 28th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks for the pointer. Hm, that's a long text (with a weird but also truncated graphics on top?).

   Thanks for the pointer. Hm, that’s a long text (with a weird but also truncated graphics on top?).

7. • CommentRowNumber7.
   • CommentAuthorDavid_Corfield
   • CommentTimeJul 28th 2021
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexJamneshan poses a question to the audience at 1:02:20 in his [talk](https://www.youtube.com/watch?v=d94jIahj2JQ&ab_channel=ToposInstitute) about relating external constructions to internal ones. Is that something to do with working in the slice over the base measure space $\Omega$?

   Jamneshan poses a question to the audience at 1:02:20 in his talk about relating external constructions to internal ones. Is that something to do with working in the slice over the base measure space $\Omega$?

8. • CommentRowNumber8.
   • CommentAuthorDmitri Pavlov
   • CommentTime1 hour ago
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded: ## Categories of measure theory From the [[nPOV]], it is desirable to have a good [[category]] for [[measure theory]]. The article [[categories of measure theory]] provides evidence that the category of compact strictly localizable [[enhanced measurable spaces]] captures the desired features of measure theory as presented in common textbooks on real analysis. <a href="https://ncatlab.org/nlab/revision/diff/measure+theory/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/measure+theory/16">v16</a>, <a href="https://ncatlab.org/nlab/show/measure+theory">current</a>

   Added:

   Categories of measure theory

   From the nPOV, it is desirable to have a good category for measure theory.

   The article categories of measure theory provides evidence that the category of compact strictly localizable enhanced measurable spaces captures the desired features of measure theory as presented in common textbooks on real analysis.

   diff, v16, current