Question

Proving the convergence of limit of the integral

score 529 · Answer 1 · 2026-04-29 15:20:26

529

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Proving the convergence of limit of the integral

Published on 29 Apr 2026 - 15:20

score 374 · Answer 2 · 2026-04-15 22:36:03

374

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To prove $f=0$ a.e under certain condition

Published on 15 Apr 2026 - 22:36

score 1.1k · Answer 3 · 2026-04-12 07:46:42

1.1k

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Does Absolute Improper Integrability imply Lebesgue Integrability?

Published on 12 Apr 2026 - 7:46

score 1.8k · Answer 4 · 2026-04-29 15:20:13

1.8k

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Convergence in $L^1$ and uniformly bounded in $L^2$ implies limit is in $L^2$

Published on 29 Apr 2026 - 15:20

score 505 · Answer 5 · 2026-04-29 15:19:26

505

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Prove that $L^{\infty}(\mathbb R)\cap C(\mathbb R)$ is not dense in $L^{\infty}(\mathbb R)$

Published on 29 Apr 2026 - 15:19

score 303 · Answer 6 · 2026-04-29 15:22:14

303

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If $f_{n}\to f$ a.e on $[0,1]$ and $f_{n}, f \in L^{p}[0,1]$ , then for all $g \in L^{q}[0,1]$ show that $\int f_{n}.g \to \int f.g$

Published on 29 Apr 2026 - 15:22

score 386 · Answer 7 · 2026-04-16 18:32:44

386

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Is the sequence $f_n(x)=\sqrt{n}\chi_{[0,1/n]}(x)$ uniformly integrable? prove or disprove

Published on 16 Apr 2026 - 18:32

score 286 · Answer 8 · 2026-04-15 17:58:09

286

Views

If $f_{n}$ belongs to and is bounded as subset of $L^{p+\theta}$ for some $\theta>0$, then $f_{n}\to f$ in $L^{p}$.

Published on 15 Apr 2026 - 17:58

score 232 · Answer 9 · 2026-04-10 12:06:55

232

Views

Commutation of limits and integral

Published on 10 Apr 2026 - 12:06

score 482 · Answer 10 · 2026-04-29 15:20:26

482

Views

Convergence in $L_1$ and uniformly bounded in $L^2$ implies convergence in $L^p$, $1<p<2$.

Published on 29 Apr 2026 - 15:20

score 739 · Answer 11 · 2026-04-29 16:17:50

739

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Problem 15.17 from the book-Real Analysis for Graduate Students by Richard Bass

Published on 29 Apr 2026 - 16:17

score 849 · Answer 12 · 2026-04-12 01:08:52

849

Views

Leibniz integral rule for distributions

Published on 12 Apr 2026 - 1:08

score 106 · Answer 13 · 2026-04-12 05:19:09

106

Views

If two measures are equal as distributions, are they equal as measures?

Published on 12 Apr 2026 - 5:19

score 43 · Answer 14 · 2026-04-11 12:57:34

43

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Finding the null sets of a continuous linear functional

Published on 11 Apr 2026 - 12:57

score 929 · Answer 15 · 2026-04-29 16:15:26

929

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Indicator function and weak convergence

Published on 29 Apr 2026 - 16:15

List Question

Proving the convergence of limit of the integral

To prove $f=0$ a.e under certain condition

Does Absolute Improper Integrability imply Lebesgue Integrability?

Convergence in $L^1$ and uniformly bounded in $L^2$ implies limit is in $L^2$

Prove that $L^{\infty}(\mathbb R)\cap C(\mathbb R)$ is not dense in $L^{\infty}(\mathbb R)$

If $f_{n}\to f$ a.e on $[0,1]$ and $f_{n}, f \in L^{p}[0,1]$ , then for all $g \in L^{q}[0,1]$ show that $\int f_{n}.g \to \int f.g$

Is the sequence $f_n(x)=\sqrt{n}\chi_{[0,1/n]}(x)$ uniformly integrable? prove or disprove

If $f_{n}$ belongs to and is bounded as subset of $L^{p+\theta}$ for some $\theta>0$, then $f_{n}\to f$ in $L^{p}$.

Commutation of limits and integral

Convergence in $L_1$ and uniformly bounded in $L^2$ implies convergence in $L^p$, $1<p<2$.

Problem 15.17 from the book-Real Analysis for Graduate Students by Richard Bass

Leibniz integral rule for distributions

If two measures are equal as distributions, are they equal as measures?

Finding the null sets of a continuous linear functional

Indicator function and weak convergence

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