Question

Does the weak limit of a sequence in $L^2([0,1])$ vanish on the limit set of vanishing sets?

score 40 · Answer 1 · 2026-04-12 22:51:16

40

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Does the weak limit of a sequence in $L^2([0,1])$ vanish on the limit set of vanishing sets?

Published on 12 Apr 2026 - 22:51

score 36 · Answer 2 · 2026-04-12 22:54:38

36

Views

With finite $\mu$, suppose $f_n$ converges in measure to $f$, and for all $n$, $||f_n||_2\leq 1$. Prove $||f_n-f||_1\rightarrow 0$

Published on 12 Apr 2026 - 22:54

score 43 · Answer 3 · 2026-04-09 21:14:43

43

Views

Lebesgue Integral help

Published on 09 Apr 2026 - 21:14

score 128 · Answer 4 · 2024-03-16 21:17:40

128

Views

Proving the equality case of the Rising Sun Inequality

Published on 16 Mar 2024 - 21:17

score 84 · Answer 5 · 2024-03-17 11:50:25

84

Views

Show that $||f_n-f||_p \rightarrow 0$ as $n \rightarrow \infty$

Published on 17 Mar 2024 - 11:50

score 69 · Answer 6 · 2026-04-09 17:59:45

69

Views

Direct method with integral constraint

Published on 09 Apr 2026 - 17:59

score 39 · Answer 7 · 2026-04-13 17:18:39

39

Views

Prove $F(x) = \int_{-\infty}^x f(t) dt$ is uniformly continuous.

Published on 13 Apr 2026 - 17:18

score 14 · Answer 8 · 2026-03-02 07:10:39

14

Views

Integral estimate with Young's inequality

Published on 02 Mar 2026 - 7:10

score 45 · Answer 9 · 2026-04-09 00:09:01

45

Views

Definition of Lebesgue integral in Stein

Published on 09 Apr 2026 - 0:09

score 62 · Answer 10 · 2026-04-02 15:16:02

62

Views

How to prove that ${\displaystyle \, \, \lim_{r \to 0} \, \sup_{x \in \mathbb R^n} \, r^{-\lambda} \int_{B(x,r)} |f_\alpha(y)|^p \, dy = 0}$?

Published on 02 Apr 2026 - 15:16

score 51 · Answer 11 · 2026-04-13 17:36:17

51

Views

Lebesgue Integral Graphical Picture/Video

Published on 13 Apr 2026 - 17:36

score 35 · Answer 12 · 2026-04-09 04:05:07

35

Views

How to do change of variable to polar coordinates in higher dimensions double integral?

Published on 09 Apr 2026 - 4:05

score 62 · Answer 13 · 2026-04-14 04:25:42

62

Views

About convergent sequence $f_n \to f$ in $L^p(U)$ ( Convergence in norm, passage of limit under integral etc.. ; Evans's PDE )

Published on 14 Apr 2026 - 4:25

score 103 · Answer 14 · 2026-04-14 09:05:57

103

Views

How to prove that $ {\displaystyle \sup_{x \in \mathbb R^n, \, r > 0} r^{-\lambda} \int_{B(x,r)} |f_\alpha(y)|^p \, dy < \infty}$?

Published on 14 Apr 2026 - 9:05

score 24 · Answer 15 · 2024-03-26 21:55:28

24

Views

prove that $\int_{A \cup B} f \, dm + \int_{A \cap B} f \, dm =\int_{B} f \, dm+ \int_{A } f \, dm$

Published on 26 Mar 2024 - 21:55

List Question

Does the weak limit of a sequence in $L^2([0,1])$ vanish on the limit set of vanishing sets?

With finite $\mu$, suppose $f_n$ converges in measure to $f$, and for all $n$, $||f_n||_2\leq 1$. Prove $||f_n-f||_1\rightarrow 0$

Lebesgue Integral help

Proving the equality case of the Rising Sun Inequality

Show that $||f_n-f||_p \rightarrow 0$ as $n \rightarrow \infty$

Direct method with integral constraint

Prove $F(x) = \int_{-\infty}^x f(t) dt$ is uniformly continuous.

Integral estimate with Young's inequality

Definition of Lebesgue integral in Stein

How to prove that ${\displaystyle \, \, \lim_{r \to 0} \, \sup_{x \in \mathbb R^n} \, r^{-\lambda} \int_{B(x,r)} |f_\alpha(y)|^p \, dy = 0}$?

Lebesgue Integral Graphical Picture/Video

How to do change of variable to polar coordinates in higher dimensions double integral?

About convergent sequence $f_n \to f$ in $L^p(U)$ ( Convergence in norm, passage of limit under integral etc.. ; Evans's PDE )

How to prove that $ {\displaystyle \sup_{x \in \mathbb R^n, \, r > 0} r^{-\lambda} \int_{B(x,r)} |f_\alpha(y)|^p \, dy < \infty}$?

prove that $\int_{A \cup B} f \, dm + \int_{A \cap B} f \, dm =\int_{B} f \, dm+ \int_{A } f \, dm$

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