Question

If $g \in \mathcal{Re}(\lambda f)$, then $|\int fd\mu| = \int gd\mu $ and $i\int \mathcal{Im}(\lambda f)d\mu = 0$

score 38 · Answer 1 · 2026-04-14 17:05:20

38

Views

If $g \in \mathcal{Re}(\lambda f)$, then $|\int fd\mu| = \int gd\mu $ and $i\int \mathcal{Im}(\lambda f)d\mu = 0$

Published on 14 Apr 2026 - 17:05

score 88 · Answer 2 · 2026-05-10 15:33:55

88

Views

Finding the values of $a$ and $\alpha$ for which the integral exists

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score 172 · Answer 3 · 2026-05-10 15:31:40

172

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Integration of the exponential radial function

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score 1.7k · Answer 4 · 2026-04-14 05:37:59

1.7k

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score 625 · Answer 5 · 2026-05-03 17:35:24

625

Views

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score 303 · Answer 6 · 2026-04-14 18:24:55

303

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score 58 · Answer 7 · 2026-04-30 16:58:26

58

Views

Lebesgue's monotone convergence theorem, - boundedness

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score 65 · Answer 8 · 2026-04-17 13:29:42

65

Views

$\lim\limits_{n\rightarrow \infty} f_n = f$ ,$f_n\in L^1(X,\mathcal{F},\mu)$ and $\int|f_n|\,\mathrm{d}\mu<M$ for all $f_n$ then $f\in L^1$

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score 76 · Answer 9 · 2026-04-11 20:27:50

76

Views

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score 77 · Answer 10 · 2026-05-10 15:12:03

77

Views

$L_{\infty}$ and simple function

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score 114 · Answer 11 · 2026-04-17 07:19:04

114

Views

If $\int_a^b g(x)dx = 0$, then $g(x) = 0$ for a.e. $x$

Published on 17 Apr 2026 - 7:19

score 81 · Answer 12 · 2026-04-29 12:27:26

81

Views

Calculate $\int_{\mathbb R^3} x_3^2 e^{-\lVert x \rVert _2} \lambda_3(dx)$

Published on 29 Apr 2026 - 12:27

score 88 · Answer 13 · 2026-04-14 09:32:55

88

Views

Calculating $\int^{\infty}_{0}\frac{e^{-y}sin^2(y)}{y}dy$

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score 290 · Answer 14 · 2026-04-13 00:48:38

290

Views

limit of $L^p$ function that does not converge in $L^p$

Published on 13 Apr 2026 - 0:48

score 684 · Answer 15 · 2026-04-12 06:49:52

684

Views

inequality involving double integral (Holder + Fubini)

Published on 12 Apr 2026 - 6:49

List Question

If $g \in \mathcal{Re}(\lambda f)$, then $|\int fd\mu| = \int gd\mu $ and $i\int \mathcal{Im}(\lambda f)d\mu = 0$

Finding the values of $a$ and $\alpha$ for which the integral exists

Integration of the exponential radial function

Lebesgue integrable implies Riemann integrable?

Distance metric limits to 0 if and only if convergence in measure

Using Taylor Series in Lebesgue Integral.

Lebesgue's monotone convergence theorem, - boundedness

$\lim\limits_{n\rightarrow \infty} f_n = f$ ,$f_n\in L^1(X,\mathcal{F},\mu)$ and $\int|f_n|\,\mathrm{d}\mu<M$ for all $f_n$ then $f\in L^1$

Application dominated convergence

$L_{\infty}$ and simple function

If $\int_a^b g(x)dx = 0$, then $g(x) = 0$ for a.e. $x$

Calculate $\int_{\mathbb R^3} x_3^2 e^{-\lVert x \rVert _2} \lambda_3(dx)$

Calculating $\int^{\infty}_{0}\frac{e^{-y}sin^2(y)}{y}dy$

limit of $L^p$ function that does not converge in $L^p$

inequality involving double integral (Holder + Fubini)

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