Question

Prove that $F$ is Lebesgue measurable and $\sum_{n=1}^\infty m(E_n)\geq Km(F)$ under these conditions...

score 319 · Answer 1 · 2026-04-17 07:43:05

319

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Prove that $F$ is Lebesgue measurable and $\sum_{n=1}^\infty m(E_n)\geq Km(F)$ under these conditions...

Published on 17 Apr 2026 - 7:43

score 505 · Answer 2 · 2026-04-09 22:55:25

505

Views

Change of variable in Lebesgue integral

Published on 09 Apr 2026 - 22:55

score 105 · Answer 3 · 2026-04-15 12:06:09

105

Views

Show that $\int_0^\infty e^{-\alpha x}\big(\frac{\sin x}{x} \big)^3 \, dx $ is continuous on $(0,\infty)$

Published on 15 Apr 2026 - 12:06

score 185 · Answer 4 · 2026-04-15 17:10:26

185

Views

Prove that $F^{(n)}(z)=\int_{X}\frac{\partial^n f}{\partial z^n}(x,z)\,\mathrm{d}\mu(x)$

Published on 15 Apr 2026 - 17:10

score 259 · Answer 5 · 2026-05-04 21:19:19

259

Views

Bartle's Elements of Integration Exercise 6.J

Published on 04 May 2026 - 21:19

score 55 · Answer 6 · 2026-04-17 16:28:38

55

Views

Show that $F(x)=o(x^{1/q} )$, where $x \to +\infty$, whith $q=\frac{p-1}{p}.$

Published on 17 Apr 2026 - 16:28

score 278 · Answer 7 · 2026-04-16 05:28:04

278

Views

Absolutely continuous on every closed interval iff $\int_{\mathbb{R}}f'(t)dt = 1$

Published on 16 Apr 2026 - 5:28

score 99 · Answer 8 · 2026-04-14 17:36:51

99

Views

$h(s)=\int_{-\infty}^{\infty}f(x)g(x-s) \, dx$ show that $h$ is uniformly continuous

Published on 14 Apr 2026 - 17:36

score 199 · Answer 9 · 2026-04-16 07:26:18

199

Views

Absolutely continuous functions that fix zero and satisfies $f'(x)=2f(x)$

Published on 16 Apr 2026 - 7:26

score 162 · Answer 10 · 2026-04-14 05:04:17

162

Views

Why bother with the space $\mathcal{L}^1$ for integration when we can abstractly deal with the completion of a semi-normed space

Published on 14 Apr 2026 - 5:04

score 50 · Answer 11 · 2026-04-16 21:12:24

50

Views

Show that $f\in \mathcal{L}^p$ and $||f||_p \leqslant M.$

Published on 16 Apr 2026 - 21:12

score 38 · Answer 12 · 2026-04-17 12:32:23

38

Views

For which values of $p$ and $q$ $\int_0^{\infty} f(x) dx$ exists as a Lebesgue integral?

Published on 17 Apr 2026 - 12:32

score 1.3k · Answer 13 · 2026-04-23 00:21:14

1.3k

Views

Using an integration by parts for a Lebesgue integral

Published on 23 Apr 2026 - 0:21

score 70 · Answer 14 · 2026-04-10 20:44:33

70

Views

multi-variable rational fraction integral

Published on 10 Apr 2026 - 20:44

score 335 · Answer 15 · 2026-04-20 06:00:13

335

Views

Show that the laplace transform is continuously differentiable

Published on 20 Apr 2026 - 6:00

List Question

Prove that $F$ is Lebesgue measurable and $\sum_{n=1}^\infty m(E_n)\geq Km(F)$ under these conditions...

Change of variable in Lebesgue integral

Show that $\int_0^\infty e^{-\alpha x}\big(\frac{\sin x}{x} \big)^3 \, dx $ is continuous on $(0,\infty)$

Prove that $F^{(n)}(z)=\int_{X}\frac{\partial^n f}{\partial z^n}(x,z)\,\mathrm{d}\mu(x)$

Bartle's Elements of Integration Exercise 6.J

Show that $F(x)=o(x^{1/q} )$, where $x \to +\infty$, whith $q=\frac{p-1}{p}.$

Absolutely continuous on every closed interval iff $\int_{\mathbb{R}}f'(t)dt = 1$

$h(s)=\int_{-\infty}^{\infty}f(x)g(x-s) \, dx$ show that $h$ is uniformly continuous

Absolutely continuous functions that fix zero and satisfies $f'(x)=2f(x)$

Why bother with the space $\mathcal{L}^1$ for integration when we can abstractly deal with the completion of a semi-normed space

Show that $f\in \mathcal{L}^p$ and $||f||_p \leqslant M.$

For which values of $p$ and $q$ $\int_0^{\infty} f(x) dx$ exists as a Lebesgue integral?

Using an integration by parts for a Lebesgue integral

multi-variable rational fraction integral

Show that the laplace transform is continuously differentiable

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