Mathematics
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All Questions Answers
Score Newest
question
5
If $f_n \overset{\star}{\rightharpoonup} f$ in $\sigma(E^\star, E)$, then $\|f\| \le \liminf \|f_n\|$
Jan 26, 2022
question
5
Is the hypothesis $\mu \ge 0$ redundant in Brezis's Ex 3.15?
Feb 26, 2022
question
4
Counter-example: approximate an integrable function from below by a continuous function with compact support
Nov 11, 2022
question
4
A proof without using net in Brezis's Ex 3.14
Feb 24, 2022
question
4
If $X$ is infinite-dimensional normed vector space, then $\mathcal C_c(X) = \{0\}$
Nov 9, 2022
question
4
Let $\mu, \nu$ both have finite second moments and $\nu \in \Pi(\mu, \nu)$. Then the inner product $\langle \cdot, \cdot\rangle$ is $\pi$-integrable
Jun 28, 2022
question
4
If $f$ is real-valued bounded measurable and $\mu$ a complex measure, then $\left | \int_X f \mathrm d \mu \right | \le \int_X |f| \mathrm d |\mu|$
Nov 9, 2022
question
4
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 $\frac{1}{p} + \frac{1}{p'} = 1$?
Aug 4, 2022
question
4
Hausdorff topological spaces: Is the pointwise limit of a sequence of Borel measurable functions again Borel measurable?
Oct 24, 2022
question
4
A proof that $\sum_{i=0}^{p_n-1} f(Y_{t_i^n})(X_{t_{i+1}^n}-X_{t_i^n})^2$ converges a.s. to $\int_0^t f(Y_s)\mathrm{d}\langle X, X\rangle_s$
Jan 31

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