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Analyst
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question
4
Disintegration of measures: a confusion about an existence proof from a lecture note
Oct 14, 2022
question
4
Does the existence of regular conditional measure follow from that of regular conditional distribution?
Oct 19, 2022
question
4
Vague convergence: confusion about the regularity of a signed Radon measure and that of its variation
Nov 5, 2022
question
3
Is this map (from the space of probability densities to the Wasserstein space) Lipschitz?
Feb 13, 2023
question
3
Let $g$ be the heat kernel. Are there constants $C_1, C_2>0$ such that $\frac{g(t_1, \cdot)}{t_1} \le C_1 \frac{g(C_2 t_2, \cdot)}{\sqrt{t_2}}$?
Jun 5, 2023
question
3
Is there a real/functional analytic proof of Cramér–Lévy theorem?
Jul 12, 2023
question
2
Optimal transport for applied mathematicians: how does $\varphi (x) = \inf_{y \in Y} [c(x, y) - \psi (y)] \neq -\infty$ follow in Theorem 1.37?
Jul 23, 2022
question
2
Complex Borel measures: does $\mu_n \to \mu$ weakly imply $|\mu|(\Theta) \le \liminf_n |\mu_n|(\Theta)$ for every open subset $\Theta$?
Nov 6, 2022
question
2
A version of Portmanteau theorem where $(\mu_n)_{n\in \mathbb N}$ is replaced by a net $(\mu_d)_{d\in D}$
Nov 28, 2022
question
2
A function $f_r$ where $f_r (x)$ is defined as the ratio between $f(x)$ and the average value of $f$ over $B(x, r)$
Dec 5, 2022
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6
Is the hypothesis $\mu \ge 0$ redundant in Brezis's Ex 3.15?
6
If $f$ is real-valued bounded measurable and $\mu$ a complex measure, then $\left | \int_X f \mathrm d \mu \right | \le \int_X |f| \mathrm d |\mu|$
5
If $f_n \overset{\star}{\rightharpoonup} f$ in $\sigma(E^\star, E)$, then $\|f\| \le \liminf \|f_n\|$
5
Is this a typo in Brezis's Ex 3.24?
5
Let $E$ be a Banach space, $p \in (1, \infty)$, and $L_p := L_{p}(X, \mu, E)$. Is $(L_p)^* \cong L_{p'}$ where $\frac{1}{p} + \frac{1}{p'} = 1$?