Question

For which $L^p[0,1]$, $1\le p < \infty$ does the function $n^\alpha*\chi_{[0,1/n]}$ converge weakly to 0?

score 166 · Answer 1 · 2026-04-15 12:29:13

166

Views

For which $L^p[0,1]$, $1\le p < \infty$ does the function $n^\alpha*\chi_{[0,1/n]}$ converge weakly to 0?

Published on 15 Apr 2026 - 12:29

score 138 · Answer 2 · 2026-04-14 07:39:28

138

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If $f:(0,\infty)\rightarrow\ (0,\infty)$ is a measurable function such that $\int_{0}^{\infty}f(x)\ dx=c$...

Published on 14 Apr 2026 - 7:39

score 165 · Answer 3 · 2026-04-09 05:25:37

165

Views

Positive and negative variations of a charge, which is an integral.

Published on 09 Apr 2026 - 5:25

score 2.5k · Answer 4 · 2026-04-15 17:57:23

2.5k

Views

Problem similar to folland chapter 2 problem 51.

Published on 15 Apr 2026 - 17:57

score 495 · Answer 5 · 2026-04-11 22:45:05

495

Views

Lebesgue's Dominated Convergence Theorem problem

Published on 11 Apr 2026 - 22:45

score 375 · Answer 6 · 2026-04-14 06:03:21

375

Views

How to prove that if $\forall x \in (a,b)$ Lebesgue integral $\int_{(a,x)}fd\lambda=0$, then $f(x)=0$ $\lambda$-almost everywhere?

Published on 14 Apr 2026 - 6:03

score 54 · Answer 7 · 2026-04-15 19:15:10

54

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Let $f_n\in L^2([0,1])$ and $\lvert\lvert f_n\rvert\rvert=1$ $\forall n$

Published on 15 Apr 2026 - 19:15

score 53 · Answer 8 · 2026-04-14 03:35:27

53

Views

Does this inequality hold for a Lipschitzian strictly decreasing function?

Published on 14 Apr 2026 - 3:35

score 269 · Answer 9 · 2026-04-12 09:06:23

269

Views

Question on a measurable function

Published on 12 Apr 2026 - 9:06

score 579 · Answer 10 · 2026-04-10 18:03:57

579

Views

Bounded measurable function

Published on 10 Apr 2026 - 18:03

score 1.1k · Answer 11 · 2026-04-13 17:25:40

1.1k

Views

Prove that, there exists no continuous function $f:\mathbb R\rightarrow\mathbb R$ with $f=\chi_{[0,1]}$ almost everywhere.

Published on 13 Apr 2026 - 17:25

score 193 · Answer 12 · 2026-04-14 00:20:40

193

Views

Problem concerning Lebesgue Integral.

Published on 14 Apr 2026 - 0:20

score 156 · Answer 13 · 2026-04-16 12:33:47

156

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Define $f$ on $\mathbb{R}$ by $f(x)=\sqrt{n}$ if $n\le x \le n+(1/n^2))$ for $n=1,2,\ldots$ and $f(x)=0$ otherwise.

Published on 16 Apr 2026 - 12:33

score 2.4k · Answer 14 · 2026-04-28 16:49:57

2.4k

Views

What is the Fourier series of Dirichlet function?

Published on 28 Apr 2026 - 16:49

score 1.4k · Answer 15 · 2026-04-15 14:16:29

1.4k

Views

Dense subspace of $L^{2}[0,1]$

Published on 15 Apr 2026 - 14:16

List Question

For which $L^p[0,1]$, $1\le p < \infty$ does the function $n^\alpha*\chi_{[0,1/n]}$ converge weakly to 0?

If $f:(0,\infty)\rightarrow\ (0,\infty)$ is a measurable function such that $\int_{0}^{\infty}f(x)\ dx=c$...

Positive and negative variations of a charge, which is an integral.

Problem similar to folland chapter 2 problem 51.

Lebesgue's Dominated Convergence Theorem problem

How to prove that if $\forall x \in (a,b)$ Lebesgue integral $\int_{(a,x)}fd\lambda=0$, then $f(x)=0$ $\lambda$-almost everywhere?

Let $f_n\in L^2([0,1])$ and $\lvert\lvert f_n\rvert\rvert=1$ $\forall n$

Does this inequality hold for a Lipschitzian strictly decreasing function?

Question on a measurable function

Bounded measurable function

Prove that, there exists no continuous function $f:\mathbb R\rightarrow\mathbb R$ with $f=\chi_{[0,1]}$ almost everywhere.

Problem concerning Lebesgue Integral.

Define $f$ on $\mathbb{R}$ by $f(x)=\sqrt{n}$ if $n\le x \le n+(1/n^2))$ for $n=1,2,\ldots$ and $f(x)=0$ otherwise.

What is the Fourier series of Dirichlet function?

Dense subspace of $L^{2}[0,1]$

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