Question

Proof that $\left| \int_X \mathbf{f} d\mu \right|_p \leq \int_X \left| \mathbf{f} \right|_p d\mu$ for $\mathbf{f} = (f_1, ..., f_n)$

score 46 · Answer 1 · 2019-11-07 09:03:42

46

Views

Proof that $\left| \int_X \mathbf{f} d\mu \right|_p \leq \int_X \left| \mathbf{f} \right|_p d\mu$ for $\mathbf{f} = (f_1, ..., f_n)$

Published on 07 Nov 2019 - 9:03

score 746 · Answer 2 · 2026-03-28 21:44:20

746

Views

Convolution $f*g(x)$ is continuous if $f \in L^1(\mathbb{R}^n)$ and $g \in L^\infty(\mathbb{R}^n)$

Published on 28 Mar 2026 - 21:44

score 133 · Answer 3 · 2019-11-07 10:28:53

133

Views

Intuition behind orthogonal decomposition of $L^2(\mu)$

Published on 07 Nov 2019 - 10:28

score 24 · Answer 4 · 2019-11-07 11:42:49

24

Views

Find $\int_\mathbb{R} \sum_{n=1}^\infty \frac{1}{3^n} \cdot 1_{[-2^n,2^n]} \, d\lambda$

Published on 07 Nov 2019 - 11:42

score 47 · Answer 5 · 2019-11-07 16:25:58

47

Views

Prove that if $E$ is measurable and $A \subset E$ is measurable, $\gamma$ is simple, then $\int_A \gamma = \int_E \gamma \chi_A $

Published on 07 Nov 2019 - 16:25

score 909 · Answer 6 · 2019-11-07 21:43:23

909

Views

Approximating an $L^1$ function by a sequence of step functions

Published on 07 Nov 2019 - 21:43

score 70 · Answer 7 · 2019-11-08 01:03:12

70

Views

Showing that $\lim_{n\to\infty} \int_0^1 f(g(x)^n)dx$ exists and lies in the interval $[f(0), f(1)]$

Published on 08 Nov 2019 - 1:03

score 360 · Answer 8 · 2026-03-29 06:33:42

360

Views

Proof of $\int_a^b f(x) dx = \int_a^bg(x)dx$

Published on 29 Mar 2026 - 6:33

score 76 · Answer 9 · 2026-03-25 12:48:49

76

Views

Kind of convergence theorem for nets

Published on 25 Mar 2026 - 12:48

score 449 · Answer 10 · 2026-02-23 06:38:10

449

Views

Is there an absolutely continuous function $f\in L^2$ for which $f'\not\in L^2$?

Published on 23 Feb 2026 - 6:38

score 884 · Answer 11 · 2026-04-01 14:20:51

884

Views

Poisson Kernel on the generalized upper half plane

Published on 01 Apr 2026 - 14:20

score 57 · Answer 12 · 2019-11-10 16:33:37

57

Views

Proof for nullset that does not consist of countable points.

Published on 10 Nov 2019 - 16:33

score 245 · Answer 13 · 2019-11-10 17:06:55

245

Views

Finding marginal distribution of uniform distribution on unit circle

Published on 10 Nov 2019 - 17:06

score 183 · Answer 14 · 2019-11-11 12:03:33

183

Views

Comparing the integrals of Lebesgue and Henstock-Kurzweil

Published on 11 Nov 2019 - 12:03

score 138 · Answer 15 · 2019-11-11 22:22:59

138

Views

$f$ is equal to the characteristic function

Published on 11 Nov 2019 - 22:22

List Question

Proof that $\left| \int_X \mathbf{f} d\mu \right|_p \leq \int_X \left| \mathbf{f} \right|_p d\mu$ for $\mathbf{f} = (f_1, ..., f_n)$

Convolution $f*g(x)$ is continuous if $f \in L^1(\mathbb{R}^n)$ and $g \in L^\infty(\mathbb{R}^n)$

Intuition behind orthogonal decomposition of $L^2(\mu)$

Find $\int_\mathbb{R} \sum_{n=1}^\infty \frac{1}{3^n} \cdot 1_{[-2^n,2^n]} \, d\lambda$

Prove that if $E$ is measurable and $A \subset E$ is measurable, $\gamma$ is simple, then $\int_A \gamma = \int_E \gamma \chi_A $

Approximating an $L^1$ function by a sequence of step functions

Showing that $\lim_{n\to\infty} \int_0^1 f(g(x)^n)dx$ exists and lies in the interval $[f(0), f(1)]$

Proof of $\int_a^b f(x) dx = \int_a^bg(x)dx$

Kind of convergence theorem for nets

Is there an absolutely continuous function $f\in L^2$ for which $f'\not\in L^2$?

Poisson Kernel on the generalized upper half plane

Proof for nullset that does not consist of countable points.

Finding marginal distribution of uniform distribution on unit circle

Comparing the integrals of Lebesgue and Henstock-Kurzweil

$f$ is equal to the characteristic function

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