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Results tagged with measure-theory
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user 125275
Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
7
votes
Which self homeomorphisms preserve measure on a torus, apart from affine?
As a simple example, if you take any divergence-free vector field, the flow generated by this vector field is incompressible, so preserves measures.
In fact, there are a huge number of measure preserv …
- 6,001
1
vote
(Sub)Optimality of random transport
The reference for the fact that $r$ gets matched to $F_B^{-1}(F_R(r))$ can be found in Theorem 2.9 of [1]. In one-dimensional optimal transport, this is known as the monotone map. I believe that the o …
- 6,001
4
votes
wasserstein distance between distributions with bounded ratio
Any estimate will need to incorporate the diameter of $X$. To see this, consider the interval $[0,L]$ and the distribution with density,
$$\begin{cases}
\frac{2}{L} & 0 \leq x \leq L/3 \\
…
- 6,001