Question

Integral of exponential function over a simplex

score 675 · Answer 1 · 2026-04-13 13:18:20

675

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Integral of exponential function over a simplex

Published on 13 Apr 2026 - 13:18

score 48 · Answer 2 · 2026-04-15 08:28:29

48

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integral calculate $f:[e,\infty)\to\mathbb{R}$

Published on 15 Apr 2026 - 8:28

score 831 · Answer 3 · 2026-04-12 11:27:07

831

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Delta function is not in $ L^1(\mathbb{R})$

Published on 12 Apr 2026 - 11:27

score 670 · Answer 4 · 2026-04-16 05:27:37

670

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if $\lim_{n\rightarrow\infty}\int_E|f_n|=\int_E|f|$ then $\int_E|f-f_n|\rightarrow 0$

Published on 16 Apr 2026 - 5:27

score 124 · Answer 5 · 2026-04-17 08:26:56

124

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there exists a continuous function $g$ on $\mathbb{R}$ and $\int_{\mathbb{R}}|f-g|<\epsilon$. Can we say that $g$ is uniform

Published on 17 Apr 2026 - 8:26

score 493 · Answer 6 · 2026-04-17 03:30:38

493

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$\lim_{t\rightarrow 0}\int_{-\infty}^{\infty}g(x)(f(x)-f(x+t))dx=0$

Published on 17 Apr 2026 - 3:30

score 1.1k · Answer 7 · 2026-04-16 14:54:44

1.1k

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Rudin's RCA; Exercise 3.4 Part (b) Only

Published on 16 Apr 2026 - 14:54

score 2.3k · Answer 8 · 2026-04-10 18:48:56

2.3k

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How is Lebesgue integration "partitioning the range"?

Published on 10 Apr 2026 - 18:48

score 928 · Answer 9 · 2026-04-15 22:40:45

928

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Prove that the series $\sum\limits_{n=-\infty}^{+\infty}f(x+n)$ converges absolutely for a.e. $x \in \mathbb{R}.$

Published on 15 Apr 2026 - 22:40

score 156 · Answer 10 · 2026-04-16 00:42:48

156

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Finding the derivative of $f(x)=\int_1^{\infty}\frac{e^{-xy}}{y^2}dy,\:\:\:x\in(0,\infty)$

Published on 16 Apr 2026 - 0:42

score 51 · Answer 11 · 2026-04-17 02:03:58

51

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$L^p(\Omega) \subsetneq L^q(\Omega)$ for all $1\leq q< p$ and $\Omega$?

Published on 17 Apr 2026 - 2:03

score 151 · Answer 12 · 2026-04-16 14:12:05

151

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Evaluate $\lim\limits_{n\to +\infty}\int\limits_{[0,n]}(1-\frac{x}{n})e^{\frac{x}{2}}dx$

Published on 16 Apr 2026 - 14:12

score 701 · Answer 13 · 2026-04-12 15:11:13

701

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(why) does an integrable function have to be measurable?

Published on 12 Apr 2026 - 15:11

score 46 · Answer 14 · 2026-04-16 13:08:42

46

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Prove $\liminf_{n\to \infty } \|u_n\|_{L^2}\geq \|u\|_{L^2}$ if $u_n\to u$ weakly.

Published on 16 Apr 2026 - 13:08

score 200 · Answer 15 · 2026-04-11 22:45:46

200

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Let $K(x,t):\mathbb{R}^{2}\to \mathbb{R}$ be a non-negative measurable function. Prove the following.

Published on 11 Apr 2026 - 22:45

List Question

Integral of exponential function over a simplex

integral calculate $f:[e,\infty)\to\mathbb{R}$

Delta function is not in $ L^1(\mathbb{R})$

if $\lim_{n\rightarrow\infty}\int_E|f_n|=\int_E|f|$ then $\int_E|f-f_n|\rightarrow 0$

there exists a continuous function $g$ on $\mathbb{R}$ and $\int_{\mathbb{R}}|f-g|<\epsilon$. Can we say that $g$ is uniform

$\lim_{t\rightarrow 0}\int_{-\infty}^{\infty}g(x)(f(x)-f(x+t))dx=0$

Rudin's RCA; Exercise 3.4 Part (b) Only

How is Lebesgue integration "partitioning the range"?

Prove that the series $\sum\limits_{n=-\infty}^{+\infty}f(x+n)$ converges absolutely for a.e. $x \in \mathbb{R}.$

Finding the derivative of $f(x)=\int_1^{\infty}\frac{e^{-xy}}{y^2}dy,\:\:\:x\in(0,\infty)$

$L^p(\Omega) \subsetneq L^q(\Omega)$ for all $1\leq q< p$ and $\Omega$?

Evaluate $\lim\limits_{n\to +\infty}\int\limits_{[0,n]}(1-\frac{x}{n})e^{\frac{x}{2}}dx$

(why) does an integrable function have to be measurable?

Prove $\liminf_{n\to \infty } \|u_n\|_{L^2}\geq \|u\|_{L^2}$ if $u_n\to u$ weakly.

Let $K(x,t):\mathbb{R}^{2}\to \mathbb{R}$ be a non-negative measurable function. Prove the following.

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