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Results tagged with measure-theory
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user 99418
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
2
votes
0
answers
53
views
If a probability measure is a mixture of products of its marginals, does it have finite mome...
Let $\mu$ be a Borel probability measure on $\mathbb{R}^n$. For a linear subspace $E\subset \mathbb{R}^n$, let $\mu_E$ denote the marginal of $\mu$ on $E$. The usual orthogonal complement of $E$ is de …
- 716
3
votes
Accepted
Transforming two smooth densities to the same density
This is impossible if $f$ is injective, without further assumptions such as bijective, differentiable, etc. Let $Q_1,Q_2$ be probability measures on a measurable space $(\Omega, \mathcal{F})$, and as …
- 716
2
votes
Dominating measure with bounded Radon-Nikodym density
If you are looking for probability measures, just modify @michael's answer as follows: let $\mu_n$ be the uniform measure on $[0,1/n)$. In fact, by taking 'sliding bumps' ($\mu_{m,n}$ is uniform meas …
- 716