Question

How to calculate the derivative of following integral?

score 77 · Answer 1 · 2019-04-04 02:17:05

77

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How to calculate the derivative of following integral?

Published on 04 Apr 2019 - 2:17

score 55 · Answer 2 · 2019-04-04 15:12:51

55

Views

Tips to show $\lim_{n \to \infty} \int_{X}|f|^{\frac{1}{n}}d\mu=\mu(\{f\neq0\})$

Published on 04 Apr 2019 - 15:12

score 729 · Answer 3 · 2019-04-05 10:07:17

729

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Is the space of piecewise continuous functions on $[0,1]$ complete in $L^2[0,1]$?

Published on 05 Apr 2019 - 10:07

score 110 · Answer 4 · 2019-04-07 05:44:13

110

Views

If $\int_{\mathbb R^d}K=1$ then $K_{\delta}(x)=\delta^{-d}K(\delta^{-1}x)$ is an approximate identity

Published on 07 Apr 2019 - 5:44

score 770 · Answer 5 · 2026-03-27 05:15:48

770

Views

Proof that Good Kernels are Approximations of Identity in $L^p(\mathbb R^d)$

Published on 27 Mar 2026 - 5:15

score 230 · Answer 6 · 2026-03-25 17:18:25

230

Views

Inequality for bounded locally integrable functions

Published on 25 Mar 2026 - 17:18

score 127 · Answer 7 · 2019-04-08 01:51:57

127

Views

Lower bound on the integral of averaging operator.

Published on 08 Apr 2019 - 1:51

score 481 · Answer 8 · 2026-03-27 05:15:51

481

Views

Convergence of convolution under $\| \cdot \|_\infty$ with a weaker kernel

Published on 27 Mar 2026 - 5:15

score 36 · Answer 9 · 2019-04-08 10:20:41

36

Views

Prove $\int_{B_R}f\leq C\int_{B_R}\left(\frac{1}{\vert B_r(x)\vert} \int_{B_r(x)} f \right) dx$ for some $R>0$ and all $r \in (0,R)$

Published on 08 Apr 2019 - 10:20

score 69 · Answer 10 · 2019-04-08 14:51:22

69

Views

Using one of the convergence theorems, find the limit of the following integral.

Published on 08 Apr 2019 - 14:51

score 51 · Answer 11 · 2019-04-08 18:09:37

51

Views

Convergence in $L^2$ norm with $f_n \geq 0$

Published on 08 Apr 2019 - 18:09

score 69 · Answer 12 · 2019-04-08 19:36:46

69

Views

Show that $f_n \to f$ in $L^2(d\mu)$ if $f_n \to f$ a.e., $f_n \ge 0$, $f_n \in L^2(d\mu), f \in L^2(d\mu)$

Published on 08 Apr 2019 - 19:36

score 464 · Answer 13 · 2019-04-09 07:38:31

464

Views

Proof of Scheffe lemma : question on the proof.

Published on 09 Apr 2019 - 7:38

score 68 · Answer 14 · 2019-04-09 12:48:15

68

Views

Existence of Lebesgue integrable function with extreme growth

Published on 09 Apr 2019 - 12:48

score 88 · Answer 15 · 2019-04-09 16:40:01

88

Views

Function defined by integral - continuity, integrability, differentiability

Published on 09 Apr 2019 - 16:40

List Question

How to calculate the derivative of following integral?

Tips to show $\lim_{n \to \infty} \int_{X}|f|^{\frac{1}{n}}d\mu=\mu(\{f\neq0\})$

Is the space of piecewise continuous functions on $[0,1]$ complete in $L^2[0,1]$?

If $\int_{\mathbb R^d}K=1$ then $K_{\delta}(x)=\delta^{-d}K(\delta^{-1}x)$ is an approximate identity

Proof that Good Kernels are Approximations of Identity in $L^p(\mathbb R^d)$

Inequality for bounded locally integrable functions

Lower bound on the integral of averaging operator.

Convergence of convolution under $\| \cdot \|_\infty$ with a weaker kernel

Prove $\int_{B_R}f\leq C\int_{B_R}\left(\frac{1}{\vert B_r(x)\vert} \int_{B_r(x)} f \right) dx$ for some $R>0$ and all $r \in (0,R)$

Using one of the convergence theorems, find the limit of the following integral.

Convergence in $L^2$ norm with $f_n \geq 0$

Show that $f_n \to f$ in $L^2(d\mu)$ if $f_n \to f$ a.e., $f_n \ge 0$, $f_n \in L^2(d\mu), f \in L^2(d\mu)$

Proof of Scheffe lemma : question on the proof.

Existence of Lebesgue integrable function with extreme growth

Function defined by integral - continuity, integrability, differentiability

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