Question

Show that $\int_{0}^{1}\frac{1}{1-f(t)}dt=\sum_{n=0}^{\infty}\int_{0}^{1}f(t)^n dt$.

score 61 · Answer 1 · 2026-04-16 02:11:40

61

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Show that $\int_{0}^{1}\frac{1}{1-f(t)}dt=\sum_{n=0}^{\infty}\int_{0}^{1}f(t)^n dt$.

Published on 16 Apr 2026 - 2:11

score 137 · Answer 2 · 2026-04-16 03:46:33

137

Views

Prove that there exists the limit $\lim\limits_{n \to \infty}\int_0^1\frac{e^x \cos x}{nx^2+\frac{1}{n}}dx$

Published on 16 Apr 2026 - 3:46

score 91 · Answer 3 · 2026-04-16 00:23:26

91

Views

$a_n=\frac{1}{n}\int_{0}^{\infty}e^{-\frac{t}{n}}f(t)dt\in\mathbb{R}$, then $a_n\rightarrow 1$ as $n\rightarrow\infty$

Published on 16 Apr 2026 - 0:23

score 64 · Answer 4 · 2026-04-12 05:57:26

64

Views

Monotone convergence for McShane (Lebesgue) integral (step in a proof)

Published on 12 Apr 2026 - 5:57

score 1.2k · Answer 5 · 2026-03-30 23:12:40

1.2k

Views

A Non-Counterexample to the Fubini Theorem with Counting and Lebesgue Measures

Published on 30 Mar 2026 - 23:12

score 1.3k · Answer 6 · 2026-04-12 08:09:48

1.3k

Views

Change of Variables in Lebesgue Integration

Published on 12 Apr 2026 - 8:09

score 519 · Answer 7 · 2026-04-11 22:20:05

519

Views

Proof that a continuous monotone function is a.e differentiable

Published on 11 Apr 2026 - 22:20

score 119 · Answer 8 · 2026-04-10 18:06:12

119

Views

Why does $\mu(E) = \int_E f d \mu$ define a measure?

Published on 10 Apr 2026 - 18:06

score 31 · Answer 9 · 2026-04-10 08:24:00

31

Views

Explanation behind definition of an integral with respect to a measure

Published on 10 Apr 2026 - 8:24

score 88 · Answer 10 · 2026-04-13 20:57:43

88

Views

Another way to see the behaviour of $||u||_p$ when $p\to 0$

Published on 13 Apr 2026 - 20:57

score 443 · Answer 11 · 2026-04-14 05:50:21

443

Views

Show that $\mu$ is a measure where $\mu(A)$ is the Dirac measure at $x=0$

Published on 14 Apr 2026 - 5:50

score 48 · Answer 12 · 2026-04-17 01:23:58

48

Views

Evaluate $\lim_{n \to \infty} \int_{-1}^{2} \frac{(1+t)^ne^{-nt}}{\frac{1}{n}+\ln{(1+nt^2)}}dt$

Published on 17 Apr 2026 - 1:23

score 79 · Answer 13 · 2026-04-14 22:10:05

79

Views

Limite of a sequence of integrals

Published on 14 Apr 2026 - 22:10

score 36 · Answer 14 · 2026-05-13 23:58:26

36

Views

Convergence and order

Published on 13 May 2026 - 23:58

score 28 · Answer 15 · 2026-04-16 04:01:10

28

Views

$\lim_{n \to \infty}\int_{\mathbb{R}^m}|f(x)-f(x+L_n(x))|dx = 0$

Published on 16 Apr 2026 - 4:01

List Question

Show that $\int_{0}^{1}\frac{1}{1-f(t)}dt=\sum_{n=0}^{\infty}\int_{0}^{1}f(t)^n dt$.

Prove that there exists the limit $\lim\limits_{n \to \infty}\int_0^1\frac{e^x \cos x}{nx^2+\frac{1}{n}}dx$

$a_n=\frac{1}{n}\int_{0}^{\infty}e^{-\frac{t}{n}}f(t)dt\in\mathbb{R}$, then $a_n\rightarrow 1$ as $n\rightarrow\infty$

Monotone convergence for McShane (Lebesgue) integral (step in a proof)

A Non-Counterexample to the Fubini Theorem with Counting and Lebesgue Measures

Change of Variables in Lebesgue Integration

Proof that a continuous monotone function is a.e differentiable

Why does $\mu(E) = \int_E f d \mu$ define a measure?

Explanation behind definition of an integral with respect to a measure

Another way to see the behaviour of $||u||_p$ when $p\to 0$

Show that $\mu$ is a measure where $\mu(A)$ is the Dirac measure at $x=0$

Evaluate $\lim_{n \to \infty} \int_{-1}^{2} \frac{(1+t)^ne^{-nt}}{\frac{1}{n}+\ln{(1+nt^2)}}dt$

Limite of a sequence of integrals

Convergence and order

$\lim_{n \to \infty}\int_{\mathbb{R}^m}|f(x)-f(x+L_n(x))|dx = 0$

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