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Results tagged with measure-theory
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user 46855
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
6
votes
Which sigma-ideals in a sigma-algebra are ideals of null sets?
Your question has already been excellently answered from two points of view:
(a) looking at the quotient $\sigma$-algebra (measurable sets modulo null sets): when is it a measure algebra? [Joseph Va …
- 2,213
5
votes
Accepted
Is the "continuous on compact subsets" characterization of measurable functions actually use...
Tautological answer: the cases where you know the measure of compact sets (as in section 3 of chapter IX of Bourbaki), but not the class of all measurable sets (which you then can define using the abo …
- 2,213
4
votes
Riesz's representation theorem for non-locally compact spaces
Historical notes of chapter 9 of Bourbaki's integration give the following as original reference for the case of completely regular spaces:
A. D. Alexandroff, Additive set functions in abstract space …
- 2,213
3
votes
Accepted
Non-Polish Lebesgue probability space?
When requesting inner regularity, you hit the ZFC - undecidable Cantor's continuum problem.
First note that a Lebesgue space has cardinality at most continuum since a countable collection of subsets …
- 2,213
2
votes
Tightness of Measures, Riesz Representation for locally compact spaces
A (specific and historical) complement to barcelos answer, too long to be correctly formatted as comment:
From Bourbaki's historical notes to chaper IX of integration:
A. D. Alexandroff [...] introdu …
- 2,213
1
vote
Integration on Compact Semirings
An easy answer along traditional lines is available iff the measure has "bounded variation" in a suitable sense.
To undestand this, first note that integration with values in Banach algebras (which …
- 2,213