Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options not deleted user 46855

Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.

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 …
user46855's user avatar
  • 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 …
user46855's user avatar
  • 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 …
user46855's user avatar
  • 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 …
user46855's user avatar
  • 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 …
user46855's user avatar
  • 2,213
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 …
user46855's user avatar
  • 2,213