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Results tagged with measure-theory
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user 14623
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
3
votes
1
answer
1k
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Probability measure product space
Let $(X,B,\mu)$ and $(Y,C,\nu)$ be probability spaces, and let $m$ be the product measure. Let $f:X \times Y \rightarrow [0,\infty )$ be a $B \otimes C $ measurable function, $1 < p < \infty$, and def …
- 67
2
votes
1
answer
683
views
Measurable function is Baire class 2 almost everywhere
Let $X$ be a polish space (separable completely metrizable topological space). Let $m$ be a probability measure on $X$ and $f:X \rightarrow \mathbb{R}$ a measureable function. I want to show that $f$ …
- 67
1
vote
1
answer
1k
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Support of Probability Measures on Separable Metric Spaces
Let $X$ be a separable metric space and $p$ a probability measure on the Borel Sets of $X$.
Denote $S_p$ the support of $p$, i.e. the set of points which have positive measure for any ball around the …
- 67