link to Measure Theory

]]>Added:

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.

]]>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 $\Omega$?

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

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

]]>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*

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

added pointer to

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

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)