Question

Proof of uniform continuity of the convolution.

score 600 · Answer 1 · 2026-03-25 04:40:31

600

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Proof of uniform continuity of the convolution.

Published on 25 Mar 2026 - 4:40

score 2.2k · Answer 2 · 2018-03-22 22:56:07

2.2k

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Lebesgue Integral of Integrable Function on a Subset

Published on 22 Mar 2018 - 22:56

score 44 · Answer 3 · 2026-03-25 03:04:12

44

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How to show $ \lim_{n\to \infty} ||f*\gamma_n - f||_1 = 0, \quad \forall f\in L^1(\mathbb{R}) $ where $\int_{-\infty}^\infty\gamma_n(t)dt = 1$?

Published on 25 Mar 2026 - 3:04

score 273 · Answer 4 · 2018-03-24 10:05:48

273

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When is it allowed to permute sum and integral for a sequence of measurable functions

Published on 24 Mar 2018 - 10:05

score 296 · Answer 5 · 2018-03-25 03:49:40

296

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Riemann-Lebesgue lemma for simple functions

Published on 25 Mar 2018 - 3:49

score 57 · Answer 6 · 2018-03-25 11:54:44

57

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Is it correct the following proof.

Published on 25 Mar 2018 - 11:54

score 333 · Answer 7 · 2018-03-25 15:23:47

333

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Proof that $f$ is Riemann integrable without Lebesgue criteria

Published on 25 Mar 2018 - 15:23

score 517 · Answer 8 · 2026-03-17 03:37:11

517

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If $\hat{f}\in L^2(\mathbb{R})$ then $\hat{f}$ is rapidly decreasing.

Published on 17 Mar 2026 - 3:37

score 529 · Answer 9 · 2018-03-28 18:28:03

529

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Evaluating improper integral as infinite sum of definite integrals

Published on 28 Mar 2018 - 18:28

score 218 · Answer 10 · 2018-03-29 02:04:46

218

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Show that a differentiable function $f$, where $f(x)$ and $f'(x)$ are integrable, has a value of $0$ when Lebesgue integrated over the real numbers.

Published on 29 Mar 2018 - 2:04

score 2k · Answer 11 · 2018-03-29 09:49:12

2k

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Why is the Monotone Convergence Theorem more famous than it's stronger cousin?

Published on 29 Mar 2018 - 9:49

score 36 · Answer 12 · 2018-03-31 03:09:21

36

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Prove $A(r)=\frac{1}{r^d} \int_{B(0,r)} |f(x-y)-f(y)|dy=0$ as $r \rightarrow 0$

Published on 31 Mar 2018 - 3:09

score 612 · Answer 13 · 2018-03-31 17:58:20

612

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Show that if $f(x)\leq g(x)$ for $x\in S$ and $\int_{S}f=\int_{S}g$, then $f$ and $g$ agree except on a set of measure zero.

Published on 31 Mar 2018 - 17:58

score 1.3k · Answer 14 · 2018-03-31 18:20:18

1.3k

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Difference between a Riemann integral and an integral against a measure

Published on 31 Mar 2018 - 18:20

score 1.8k · Answer 15 · 2018-03-31 19:05:25

1.8k

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For $1\leq p<q\leq\infty$ what function is in $L^p$ but not in $L^q$

Published on 31 Mar 2018 - 19:05

List Question

Proof of uniform continuity of the convolution.

Lebesgue Integral of Integrable Function on a Subset

How to show $ \lim_{n\to \infty} ||f*\gamma_n - f||_1 = 0, \quad \forall f\in L^1(\mathbb{R}) $ where $\int_{-\infty}^\infty\gamma_n(t)dt = 1$?

When is it allowed to permute sum and integral for a sequence of measurable functions

Riemann-Lebesgue lemma for simple functions

Is it correct the following proof.

Proof that $f$ is Riemann integrable without Lebesgue criteria

If $\hat{f}\in L^2(\mathbb{R})$ then $\hat{f}$ is rapidly decreasing.

Evaluating improper integral as infinite sum of definite integrals

Show that a differentiable function $f$, where $f(x)$ and $f'(x)$ are integrable, has a value of $0$ when Lebesgue integrated over the real numbers.

Why is the Monotone Convergence Theorem more famous than it's stronger cousin?

Prove $A(r)=\frac{1}{r^d} \int_{B(0,r)} |f(x-y)-f(y)|dy=0$ as $r \rightarrow 0$

Show that if $f(x)\leq g(x)$ for $x\in S$ and $\int_{S}f=\int_{S}g$, then $f$ and $g$ agree except on a set of measure zero.

Difference between a Riemann integral and an integral against a measure

For $1\leq p<q\leq\infty$ what function is in $L^p$ but not in $L^q$

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