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Results tagged with real-analysis
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user 112001
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
4
votes
1
answer
1k
views
Is the Wasserstein-1 metric translation invariant?
Define the Wasserstein-1 metric (or the Earth mover's distance) between two positive measures $\mu_1$, $\mu_2$ by
$$
W(\mu_1, \mu_2)
=
\inf_{\gamma \in \Gamma (\mu_1, \mu_2)} \int \|x_1 - x_2\| \, \m …
- 252
3
votes
0
answers
494
views
Continuity of the conditional expectation
Consider the conditional expectation of $x$ given $y$,
$$
\mathbb{E}(x | y)
$$
where $x \in X$ and $y \in Y$ where $X, Y$ are Hilbert spaces (possibly infinite dimensional).
Question :
I am looking f …
- 252