Question

For $p\geq1$, $f\in L^p(\mathbb{R}^n)$ and $\lambda>0$, does $\{x\in\mathbb{R}^n:|f(x)|>\lambda\}$ have finite measure?

score 77 · Answer 1 · 2016-11-04 14:25:01

77

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For $p\geq1$, $f\in L^p(\mathbb{R}^n)$ and $\lambda>0$, does $\{x\in\mathbb{R}^n:|f(x)|>\lambda\}$ have finite measure?

Published on 04 Nov 2016 - 14:25

score 59 · Answer 2 · 2016-11-04 14:33:41

59

Views

Trouble Finding Dominating Integrable Functions for Limiting Integrals

Published on 04 Nov 2016 - 14:33

score 43 · Answer 3 · 2016-11-04 15:11:35

43

Views

If $\left|\psi\right> \in L_2$, does $\left|\psi\right> ^2 \in L_2$

Published on 04 Nov 2016 - 15:11

score 1k · Answer 4 · 2016-11-04 16:56:33

1k

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Lebesgue integral over unions

Published on 04 Nov 2016 - 16:56

score 35 · Answer 5 · 2016-11-05 14:30:31

35

Views

Show that this function is in $L_1$

Published on 05 Nov 2016 - 14:30

score 484 · Answer 6 · 2026-03-29 11:44:15

484

Views

Finding variance of Renewal process: a particular renewal equation

Published on 29 Mar 2026 - 11:44

score 56 · Answer 7 · 2016-11-06 16:13:44

56

Views

Let $E_c:=\{x \in \mathbb R: f(x) \ge c\}$ Prove that $\int_{E_c}f\,dm \ge c\cdot m(E_c)$

Published on 06 Nov 2016 - 16:13

score 446 · Answer 8 · 2026-04-07 17:40:03

446

Views

Questions on Dominated Convergence with Dirac Deltas

Published on 07 Apr 2026 - 17:40

score 238 · Answer 9 · 2016-11-07 04:17:50

238

Views

Lebesgue Monotonous Convergence Theorem for $f_n = \chi_{[0,n]}$

Published on 07 Nov 2016 - 4:17

score 388 · Answer 10 · 2016-11-08 00:04:47

388

Views

Show that Lebesgue integral is continuous and differentiable

Published on 08 Nov 2016 - 0:04

score 123 · Answer 11 · 2016-11-08 10:47:10

123

Views

Definition of the Lebesgue integral

Published on 08 Nov 2016 - 10:47

score 164 · Answer 12 · 2026-04-02 02:13:02

164

Views

Limit of an integral related to Gamma function: $ \lim_{k \to \infty}\int_{0}^{k} x^{n}\left(1 - {x \over k}\right)^{k}\,\mathrm{d}x = n! $

Published on 02 Apr 2026 - 2:13

score 316 · Answer 13 · 2016-11-09 15:28:30

316

Views

Evaluating Lebesgue integral on the unit ball

Published on 09 Nov 2016 - 15:28

score 27 · Answer 14 · 2016-11-09 16:33:46

27

Views

If $\int_{S_2}udS=0$ can we say that $u=0$ on $S_2$?

Published on 09 Nov 2016 - 16:33

score 599 · Answer 15 · 2016-11-09 16:48:25

599

Views

Prove that $ \lim_{n \to \infty} \int_{-\infty}^{\infty} \sin(nt) f(t) d t = 0 $.

Published on 09 Nov 2016 - 16:48

List Question

For $p\geq1$, $f\in L^p(\mathbb{R}^n)$ and $\lambda>0$, does $\{x\in\mathbb{R}^n:|f(x)|>\lambda\}$ have finite measure?

Trouble Finding Dominating Integrable Functions for Limiting Integrals

If $\left|\psi\right> \in L_2$, does $\left|\psi\right> ^2 \in L_2$

Lebesgue integral over unions

Show that this function is in $L_1$

Finding variance of Renewal process: a particular renewal equation

Let $E_c:=\{x \in \mathbb R: f(x) \ge c\}$ Prove that $\int_{E_c}f\,dm \ge c\cdot m(E_c)$

Questions on Dominated Convergence with Dirac Deltas

Lebesgue Monotonous Convergence Theorem for $f_n = \chi_{[0,n]}$

Show that Lebesgue integral is continuous and differentiable

Definition of the Lebesgue integral

Limit of an integral related to Gamma function: $ \lim_{k \to \infty}\int_{0}^{k} x^{n}\left(1 - {x \over k}\right)^{k}\,\mathrm{d}x = n! $

Evaluating Lebesgue integral on the unit ball

If $\int_{S_2}udS=0$ can we say that $u=0$ on $S_2$?

Prove that $ \lim_{n \to \infty} \int_{-\infty}^{\infty} \sin(nt) f(t) d t = 0 $.

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