Question

If $f,g \in L^2([-\pi,\pi])$ and are periodic with period $2\pi$ then the convolution is integrable

score 72 · Answer 1 · 2026-04-16 06:58:01

72

Views

If $f,g \in L^2([-\pi,\pi])$ and are periodic with period $2\pi$ then the convolution is integrable

Published on 16 Apr 2026 - 6:58

score 181 · Answer 2 · 2026-04-25 10:34:48

181

Views

Cauchy sequences on $L^p$ and $L^q$

Published on 25 Apr 2026 - 10:34

score 301 · Answer 3 · 2026-04-09 15:50:29

301

Views

How to show Rademacher functions are independent.

Published on 09 Apr 2026 - 15:50

score 136 · Answer 4 · 2026-04-11 23:04:26

136

Views

The Lebesgue integral of a measurable nonnegative function.

Published on 11 Apr 2026 - 23:04

score 36 · Answer 5 · 2026-04-15 19:35:40

36

Views

Evaluate $\int\limits_{}^{}\frac{x (1-ax^2)^N}{(1/x^{\gamma}-t)^2}dx$

Published on 15 Apr 2026 - 19:35

score 30 · Answer 6 · 2026-03-31 13:08:09

30

Views

Points moving on circles in $\mathbb{R^3}$ connected with open line segments. Find parametrization in order to count integral.

Published on 31 Mar 2026 - 13:08

score 138 · Answer 7 · 2026-04-17 14:46:48

138

Views

Show that given $\epsilon>0$ there exists $E\subset\mathbb{R}$ measurable so that $\int_{\mathbb{E}}f\,dm > \int_{\mathbb{R}}f\,dm-\epsilon$

Published on 17 Apr 2026 - 14:46

score 181 · Answer 8 · 2026-04-17 13:53:50

181

Views

Sequence of measurable functions $\{g_n\}_{n=1}^{\infty}$ such that $\lim_{n\to\infty}\int_{0}^{1}f(t)g_n(t)dt=\int_0^1f(t)dt$ whenever $f\in C[0,1]$

Published on 17 Apr 2026 - 13:53

score 876 · Answer 9 · 2026-04-29 07:17:32

876

Views

Can $L^1$ functions be approximated by sequence of simple functions?

Published on 29 Apr 2026 - 7:17

score 95 · Answer 10 · 2026-04-11 16:26:36

95

Views

Lebesgue integral and monotonicity of simple functions

Published on 11 Apr 2026 - 16:26

score 173 · Answer 11 · 2026-04-15 21:36:35

173

Views

Show that $F:\mathbb{R}\rightarrow \mathbb{R}$, $F(x):=\int_{(-\infty,x]}fdm$ is continuous.

Published on 15 Apr 2026 - 21:36

score 170 · Answer 12 · 2026-04-25 10:38:14

170

Views

An example for $f\in H^1(\Omega)$ but not in $L^\infty(\Omega)$?

Published on 25 Apr 2026 - 10:38

score 59 · Answer 13 · 2026-04-16 04:48:21

59

Views

Compute $\sum_{n=0}^{\infty}\int_{0}^{\pi/2}(1-\sqrt{\sin(x)})^{n}\cos(x)dx$

Published on 16 Apr 2026 - 4:48

score 2k · Answer 14 · 2026-04-14 11:43:33

2k

Views

Does the graph of a measurable function always have zero measure?

Published on 14 Apr 2026 - 11:43

score 34 · Answer 15 · 2026-04-10 16:39:48

34

Views

The Lebesgue Integral

Published on 10 Apr 2026 - 16:39

List Question

If $f,g \in L^2([-\pi,\pi])$ and are periodic with period $2\pi$ then the convolution is integrable

Cauchy sequences on $L^p$ and $L^q$

How to show Rademacher functions are independent.

The Lebesgue integral of a measurable nonnegative function.

Evaluate $\int\limits_{}^{}\frac{x (1-ax^2)^N}{(1/x^{\gamma}-t)^2}dx$

Points moving on circles in $\mathbb{R^3}$ connected with open line segments. Find parametrization in order to count integral.

Show that given $\epsilon>0$ there exists $E\subset\mathbb{R}$ measurable so that $\int_{\mathbb{E}}f\,dm > \int_{\mathbb{R}}f\,dm-\epsilon$

Sequence of measurable functions $\{g_n\}_{n=1}^{\infty}$ such that $\lim_{n\to\infty}\int_{0}^{1}f(t)g_n(t)dt=\int_0^1f(t)dt$ whenever $f\in C[0,1]$

Can $L^1$ functions be approximated by sequence of simple functions?

Lebesgue integral and monotonicity of simple functions

Show that $F:\mathbb{R}\rightarrow \mathbb{R}$, $F(x):=\int_{(-\infty,x]}fdm$ is continuous.

An example for $f\in H^1(\Omega)$ but not in $L^\infty(\Omega)$?

Compute $\sum_{n=0}^{\infty}\int_{0}^{\pi/2}(1-\sqrt{\sin(x)})^{n}\cos(x)dx$

Does the graph of a measurable function always have zero measure?

The Lebesgue Integral

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