Question

What is the difference of - $L^p$ spaces - defined using extended real line and real line functions?

score 413 · Answer 1 · 2026-04-15 02:02:47

413

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What is the difference of - $L^p$ spaces - defined using extended real line and real line functions?

Published on 15 Apr 2026 - 2:02

score 44 · Answer 2 · 2026-04-12 01:33:24

44

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Trivial Equality in Lebesgue Decomposition

Published on 12 Apr 2026 - 1:33

score 56 · Answer 3 · 2026-04-16 05:09:08

56

Views

Need help with parametrization and finding $\int_{K,+}(x+\sqrt{z})dy+(x+\sqrt{y})dy$ where $K=\{(x,y,z):y+z=5x^2,yz=4x^2,y\leq z\,-2\leq x\leq 1\}$

Published on 16 Apr 2026 - 5:09

score 533 · Answer 4 · 2026-04-12 13:27:33

533

Views

Is the function $f(x,y)$ integrable (Fubini Tonelli).

Published on 12 Apr 2026 - 13:27

score 415 · Answer 5 · 2026-04-18 15:15:38

415

Views

A problem related to monotone convergence theorem in measure theory.

Published on 18 Apr 2026 - 15:15

score 37 · Answer 6 · 2026-04-14 17:06:12

37

Views

If $\int_{X}f\; d\mu = \int_{X}|f|\; d\mu$ then $v$ in $f = u+iv$ is a zero function.

Published on 14 Apr 2026 - 17:06

score 572 · Answer 7 · 2026-04-18 15:15:36

572

Views

Prove that $\lim_{n\to\infty}\int f_n=\int f$.

Published on 18 Apr 2026 - 15:15

score 96 · Answer 8 · 2026-04-16 11:59:22

96

Views

$\int_{A_n} f(x) d\mu$ converge to $\int_{A } f(x) d\mu$?

Published on 16 Apr 2026 - 11:59

score 51 · Answer 9 · 2026-04-16 11:50:11

51

Views

$\sum_n \int_{A_n} |f(x)| d\mu < \infty $

Published on 16 Apr 2026 - 11:50

score 146 · Answer 10 · 2026-04-16 13:44:29

146

Views

Show that $\lim_{n\rightarrow\infty}\int_{0}^{\infty}\frac{x^{\frac{1}{n}}}{(1+\frac{x}{n})^{n}}dx=1.$

Published on 16 Apr 2026 - 13:44

score 278 · Answer 11 · 2026-04-15 03:33:22

278

Views

Let $\lambda_2=\lambda \otimes \lambda$ be the product lebesgue measure. Is the unit disk $\lambda_2$-measurable?

Published on 15 Apr 2026 - 3:33

score 204 · Answer 12 · 2026-04-14 14:42:23

204

Views

Finding a non-negative Lebesgue measurable function such that $||f_n ||_2 \rightarrow \infty$ and $||\sqrt{f_n}||_2\leq 1$.

Published on 14 Apr 2026 - 14:42

score 336 · Answer 13 · 2026-04-11 16:26:26

336

Views

Lebesgue integrability of a function over the real line

Published on 11 Apr 2026 - 16:26

score 50 · Answer 14 · 2026-04-15 06:18:51

50

Views

Find an example of two measurable functions such that $h \in \mathcal{L_1}(\mathbb{R})$ and $h \notin \mathcal{L_1}(\mathbb{R})$.

Published on 15 Apr 2026 - 6:18

score 97 · Answer 15 · 2026-04-17 12:09:01

97

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Consider a measurable function $f:[0,1]\rightarrow \mathbb{R}$ such that $f(x)\geq ||f||_2$.

Published on 17 Apr 2026 - 12:09

List Question

What is the difference of - $L^p$ spaces - defined using extended real line and real line functions?

Trivial Equality in Lebesgue Decomposition

Need help with parametrization and finding $\int_{K,+}(x+\sqrt{z})dy+(x+\sqrt{y})dy$ where $K=\{(x,y,z):y+z=5x^2,yz=4x^2,y\leq z\,-2\leq x\leq 1\}$

Is the function $f(x,y)$ integrable (Fubini Tonelli).

A problem related to monotone convergence theorem in measure theory.

If $\int_{X}f\; d\mu = \int_{X}|f|\; d\mu$ then $v$ in $f = u+iv$ is a zero function.

Prove that $\lim_{n\to\infty}\int f_n=\int f$.

$\int_{A_n} f(x) d\mu$ converge to $\int_{A } f(x) d\mu$?

$\sum_n \int_{A_n} |f(x)| d\mu < \infty $

Show that $\lim_{n\rightarrow\infty}\int_{0}^{\infty}\frac{x^{\frac{1}{n}}}{(1+\frac{x}{n})^{n}}dx=1.$

Let $\lambda_2=\lambda \otimes \lambda$ be the product lebesgue measure. Is the unit disk $\lambda_2$-measurable?

Finding a non-negative Lebesgue measurable function such that $||f_n ||_2 \rightarrow \infty$ and $||\sqrt{f_n}||_2\leq 1$.

Lebesgue integrability of a function over the real line

Find an example of two measurable functions such that $h \in \mathcal{L_1}(\mathbb{R})$ and $h \notin \mathcal{L_1}(\mathbb{R})$.

Consider a measurable function $f:[0,1]\rightarrow \mathbb{R}$ such that $f(x)\geq ||f||_2$.

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