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

7 votes
2 answers
1k views

Sections measure zero imply set is measure zero?

I have a subset $B\subset\mathbb{R}^n\times\mathbb{R}^m$ that I want to show has measure zero. I know that the sections $B^x = \{y : (x,y)\in B\}$ all have measure zero. I do not know if $B$ is measur …
1 vote
3 answers
1k views

What does it mean to say "almost always" ?

I have a set, $A$, of $m \times n$ matrices with certain properties and a subset $B$ of $A$. I would like to say that when randomly selecting such a matrix, I am "almost always" never in $B$. I can sh …