Question

Poitwise limit of a monotonically increasing function sequence in $L^p(M)$ exists always almost everywhere

score 28 · Answer 1 · 2026-04-15 05:09:05

28

Views

Poitwise limit of a monotonically increasing function sequence in $L^p(M)$ exists always almost everywhere

Published on 15 Apr 2026 - 5:09

score 244 · Answer 2 · 2026-04-15 13:41:44

244

Views

Prove $L^p$ ($1\leqslant p\leq +\infty)$ Norms on $C[0,1]$ are Not Equivalent

Published on 15 Apr 2026 - 13:41

score 70 · Answer 3 · 2026-04-15 00:05:54

70

Views

Let $\mu$ be a probability measure. Prove that, function $f$ is $L^1$ iff $f=g\bar{h}$ for some $g,h\in L^2$.

Published on 15 Apr 2026 - 0:05

score 38 · Answer 4 · 2026-04-14 00:11:31

38

Views

Specific Norms Not Equivalent on $C_b(\mathbb{R})$

Published on 14 Apr 2026 - 0:11

score 52 · Answer 5 · 2026-05-15 08:36:55

52

Views

Prove $u|_{\bar\Omega_j} \in C^1(\bar \Omega_j)$ such that $u \in H^1(\Omega)$ belongs to $C(\bar\Omega)$

Published on 15 May 2026 - 8:36

score 462 · Answer 6 · 2026-05-15 08:39:32

462

Views

Functions in Sobolev Spaces that are NOT continuous

Published on 15 May 2026 - 8:39

score 27 · Answer 7 · 2026-04-16 00:24:31

27

Views

If $(f_n)$ is bounded in $L^p$ then $\int_{B_r^C}|f_n|^p dx\to 0$ uniformly in $n$ if $r\to \infty$?

Published on 16 Apr 2026 - 0:24

score 50 · Answer 8 · 2026-04-16 11:17:31

50

Views

Convergence in $L^1$ and boundedness in $L^{\infty}$ imply strong convergence in $L^p$ for $1<p<\infty$?

Published on 16 Apr 2026 - 11:17

score 110 · Answer 9 · 2026-04-14 09:33:37

110

Views

Version of Lebesgue differentiation theorem

Published on 14 Apr 2026 - 9:33

score 142 · Answer 10 · 2026-04-15 20:36:26

142

Views

Generalization of Riesz Representation theorem for $L^p$ spaces

Published on 15 Apr 2026 - 20:36

score 143 · Answer 11 · 2026-04-14 07:04:48

143

Views

Show that $T$ in $l^{\infty}$ to $l^p$ is well defined and compute the operator norm $∥T∥$.

Published on 14 Apr 2026 - 7:04

score 46 · Answer 12 · 2026-04-15 22:48:55

46

Views

$L^1$ approximation of $f \circ g$

Published on 15 Apr 2026 - 22:48

score 41 · Answer 13 · 2026-04-15 15:42:31

If $f$ is continuous on $\mathbb{R}$ and $f\to 0$ when $x\to \pm \infty$, is $f\in L^p(\mathbb{R})$ for some $1\leqslant p <\infty$?

score 111 · Answer 14 · 2026-05-15 01:28:05

111

Views

Inner Product on Schwartz Space and $L^2$

Published on 15 May 2026 - 1:28

score 113 · Answer 15 · 2026-04-16 13:21:52

113

Views

Compute $\lim_\limits{n \to \infty} \int_{0}^{1} f_n\,\mathrm d\lambda$

Published on 16 Apr 2026 - 13:21

List Question

Poitwise limit of a monotonically increasing function sequence in $L^p(M)$ exists always almost everywhere

Prove $L^p$ ($1\leqslant p\leq +\infty)$ Norms on $C[0,1]$ are Not Equivalent

Let $\mu$ be a probability measure. Prove that, function $f$ is $L^1$ iff $f=g\bar{h}$ for some $g,h\in L^2$.

Specific Norms Not Equivalent on $C_b(\mathbb{R})$

Prove $u|_{\bar\Omega_j} \in C^1(\bar \Omega_j)$ such that $u \in H^1(\Omega)$ belongs to $C(\bar\Omega)$

Functions in Sobolev Spaces that are NOT continuous

If $(f_n)$ is bounded in $L^p$ then $\int_{B_r^C}|f_n|^p dx\to 0$ uniformly in $n$ if $r\to \infty$?

Convergence in $L^1$ and boundedness in $L^{\infty}$ imply strong convergence in $L^p$ for $1<p<\infty$?

Version of Lebesgue differentiation theorem

Generalization of Riesz Representation theorem for $L^p$ spaces

Show that $T$ in $l^{\infty}$ to $l^p$ is well defined and compute the operator norm $∥T∥$.

$L^1$ approximation of $f \circ g$

If $f$ is continuous on $\mathbb{R}$ and $f\to 0$ when $x\to \pm \infty$, is $f\in L^p(\mathbb{R})$ for some $1\leqslant p <\infty$?

Inner Product on Schwartz Space and $L^2$

Compute $\lim_\limits{n \to \infty} \int_{0}^{1} f_n\,\mathrm d\lambda$

Trending Questions

Popular # Hahtags

Popular Questions