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Results tagged with measure-theory
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user 123897
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
3
votes
Effect of perturbing the atoms of a measure on the Wasserstein distance
Without further constraints this is not true and easy to see if $X$ is Euclidean: Let $\Gamma$ be the support of an optimal coupling between $G$ and $G'$. If for fixed $y\in p_2(\Gamma)$ the set $\{x …
- 576
1
vote
Accepted
Echange of Infimum Integral with Pointwise Infimum
If $U$ is non-empty then the value of either side is $m \mu(\mathcal{X})$ where $m= \inf \{y^2 ~|~ g(y)<M\}$. If $\mu$ is non-finite then $m=0$.
To see this note first that for $f_1,f_2 \in U$ the f …
- 576