Question

Prove that there exists $h \in L^1(\mu)$ such that $h \geq 0$ and $\int f \circ T = \int fh$

score 99 · Answer 1 · 2026-04-15 04:46:57

99

Views

Prove that there exists $h \in L^1(\mu)$ such that $h \geq 0$ and $\int f \circ T = \int fh$

Published on 15 Apr 2026 - 4:46

score 389 · Answer 2 · 2026-04-14 21:21:42

389

Views

Why any uncountable $G_\delta$ set of $\mathbb{R}$, has a subset homeomorphic to $[0,1]$

Published on 14 Apr 2026 - 21:21

score 301 · Answer 3 · 2026-04-10 12:27:56

301

Views

Lebesgue measure and integral

Published on 10 Apr 2026 - 12:27

score 450 · Answer 4 · 2026-04-11 17:21:09

450

Views

Theory of "integration" on sets of measure zero (the measure zero sets are with respect to Lebesgue measure )

Published on 11 Apr 2026 - 17:21

score 84 · Answer 5 · 2026-04-15 10:54:08

84

Views

Show that $\int_0^\infty f du = \lim_{⁡n\to\infty}\int_0^n fdu$

Published on 15 Apr 2026 - 10:54

score 136 · Answer 6 · 2026-04-15 18:10:56

136

Views

Compute $\lim_{n\rightarrow \infty} n\int_0^1(1+x)^n e^{-3nx} \mathrm{d} \mu (x)$

Published on 15 Apr 2026 - 18:10

score 111 · Answer 7 · 2026-04-11 00:17:56

111

Views

Exercise of integration

Published on 11 Apr 2026 - 0:17

score 89 · Answer 8 · 2026-04-12 02:45:42

89

Views

Enumerable unions and Lebesgue measure; Result from Macbeath & Rogers

Published on 12 Apr 2026 - 2:45

score 195 · Answer 9 · 2026-04-17 03:37:33

195

Views

Computation of $\lim_{n \rightarrow \infty} n(\int_{0}^{\infty} \frac{1}{1+x^4+x^n} \mathrm{d}m(x)-C)$

Published on 17 Apr 2026 - 3:37

score 3.1k · Answer 10 · 2026-04-15 00:01:33

3.1k

Views

Notation used for integrals w.r.t. probability measures

Published on 15 Apr 2026 - 0:01

score 202 · Answer 11 · 2026-04-10 03:17:17

202

Views

Lebesgue Integral: calculation of limit

Published on 10 Apr 2026 - 3:17

score 113 · Answer 12 · 2026-04-13 11:58:52

113

Views

Question of Lebesgue integrals to show functions are the same \mu a.e

Published on 13 Apr 2026 - 11:58

score 93 · Answer 13 · 2026-04-18 15:07:48

93

Views

Question about integrable functions and integrands

Published on 18 Apr 2026 - 15:07

score 107 · Answer 14 · 2026-04-16 10:17:31

107

Views

WTS $\int|f(t+s)-f(t)|dt\rightarrow ?$ as $s\rightarrow 0$

Published on 16 Apr 2026 - 10:17

score 424 · Answer 15 · 2026-04-10 01:16:30

424

Views

Convergence in $L^1$ of defined step functions

Published on 10 Apr 2026 - 1:16

List Question

Prove that there exists $h \in L^1(\mu)$ such that $h \geq 0$ and $\int f \circ T = \int fh$

Why any uncountable $G_\delta$ set of $\mathbb{R}$, has a subset homeomorphic to $[0,1]$

Lebesgue measure and integral

Theory of "integration" on sets of measure zero (the measure zero sets are with respect to Lebesgue measure )

Show that $\int_0^\infty f du = \lim_{⁡n\to\infty}\int_0^n fdu$

Compute $\lim_{n\rightarrow \infty} n\int_0^1(1+x)^n e^{-3nx} \mathrm{d} \mu (x)$

Exercise of integration

Enumerable unions and Lebesgue measure; Result from Macbeath & Rogers

Computation of $\lim_{n \rightarrow \infty} n(\int_{0}^{\infty} \frac{1}{1+x^4+x^n} \mathrm{d}m(x)-C)$

Notation used for integrals w.r.t. probability measures

Lebesgue Integral: calculation of limit

Question of Lebesgue integrals to show functions are the same \mu a.e

Question about integrable functions and integrands

WTS $\int|f(t+s)-f(t)|dt\rightarrow ?$ as $s\rightarrow 0$

Convergence in $L^1$ of defined step functions

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