Question

Can we show $\int_{B_i}\left|f-\frac1{λ(B_i)}\int_{B_i}f\:{\rm d}λ\right|^2\:{\rm d}λ\le\int\left|f-\frac1{λ(B)}\int f\:{\rm d}λ\right|^2\:{\rm d}λ$?

score 80 · Answer 1 · 2026-03-26 19:19:58

80

Views

Can we show $\int_{B_i}\left|f-\frac1{λ(B_i)}\int_{B_i}f\:{\rm d}λ\right|^2\:{\rm d}λ\le\int\left|f-\frac1{λ(B)}\int f\:{\rm d}λ\right|^2\:{\rm d}λ$?

Published on 26 Mar 2026 - 19:19

score 430 · Answer 2 · 2020-03-02 12:31:29

430

Views

Can the Dominated Convergence Theorem and MCT be used for limits to zero?

Published on 02 Mar 2020 - 12:31

score 1k · Answer 3 · 2020-03-02 14:00:10

1k

Views

Prove that a Lebesgue measurable function is almost everywhere equal to a Borel measurable function

Published on 02 Mar 2020 - 14:00

score 2.4k · Answer 4 · 2026-04-02 18:45:47

2.4k

Views

Counterexample in Fubini's Theorem (non-integrable function)

Published on 02 Apr 2026 - 18:45

score 27 · Answer 5 · 2026-03-26 19:19:58

27

Views

Can we show $\int_{B_j}λ({\rm d}y)\frac{\left|h_j(y)f(y)-\frac{λ(h_jf)}{λ(B_j)}\right|^2}{r(y)}\le\int_Bλ({\rm d}y)\frac{|f(y)-γλf|^2}{r(y)}$?

Published on 26 Mar 2026 - 19:19

score 2k · Answer 6 · 2020-03-03 01:56:46

2k

Views

Convergence In L2 norm

Published on 03 Mar 2020 - 1:56

score 33 · Answer 7 · 2026-03-28 09:44:06

33

Views

$\varepsilon$ in $\int_{-\varepsilon}^\infty e^{-x}\delta(\sin{x})\;dx$

Published on 28 Mar 2026 - 9:44

score 298 · Answer 8 · 2026-03-29 23:41:20

298

Views

Distribution-Theory: Show that a function tends to the Dirac delta function

Published on 29 Mar 2026 - 23:41

score 401 · Answer 9 · 2020-03-04 23:58:48

401

Views

Showing $\lim_{n \to \infty} \int |f_n| - |f - f_n| = \int |f|$

Published on 04 Mar 2020 - 23:58

score 242 · Answer 10 · 2026-03-26 19:27:45

242

Views

A different statement for Fubini's theorem and correcting a solution.

Published on 26 Mar 2026 - 19:27

score 29 · Answer 11 · 2020-03-05 17:54:07

29

Views

Functional having fixed point.

Published on 05 Mar 2020 - 17:54

score 123 · Answer 12 · 2020-03-05 20:14:22

123

Views

Prove $\lim_{r \to \infty}\int_{0}^{r}\frac{\sin x}{x}=\frac{\pi}{2}$ using the double integral

Published on 05 Mar 2020 - 20:14

score 169 · Answer 13 · 2026-04-02 04:48:43

169

Views

Lebesgue integration of conditional expectation

Published on 02 Apr 2026 - 4:48

score 71 · Answer 14 · 2026-03-30 00:24:41

71

Views

How to show $\|e^{ikx}-e^{ix}\|_{L^{1}}$ does not converge to $0$ when $k\rightarrow\infty$?

Published on 30 Mar 2026 - 0:24

score 91 · Answer 15 · 2026-03-27 00:03:06

91

Views

Does an integral operator from $L^2$ to $L^2$ necessarily have a square integrable kernel?

Published on 27 Mar 2026 - 0:03

List Question

Can we show $\int_{B_i}\left|f-\frac1{λ(B_i)}\int_{B_i}f\:{\rm d}λ\right|^2\:{\rm d}λ\le\int\left|f-\frac1{λ(B)}\int f\:{\rm d}λ\right|^2\:{\rm d}λ$?

Can the Dominated Convergence Theorem and MCT be used for limits to zero?

Prove that a Lebesgue measurable function is almost everywhere equal to a Borel measurable function

Counterexample in Fubini's Theorem (non-integrable function)

Can we show $\int_{B_j}λ({\rm d}y)\frac{\left|h_j(y)f(y)-\frac{λ(h_jf)}{λ(B_j)}\right|^2}{r(y)}\le\int_Bλ({\rm d}y)\frac{|f(y)-γλf|^2}{r(y)}$?

Convergence In L2 norm

$\varepsilon$ in $\int_{-\varepsilon}^\infty e^{-x}\delta(\sin{x})\;dx$

Distribution-Theory: Show that a function tends to the Dirac delta function

Showing $\lim_{n \to \infty} \int |f_n| - |f - f_n| = \int |f|$

A different statement for Fubini's theorem and correcting a solution.

Functional having fixed point.

Prove $\lim_{r \to \infty}\int_{0}^{r}\frac{\sin x}{x}=\frac{\pi}{2}$ using the double integral

Lebesgue integration of conditional expectation

How to show $\|e^{ikx}-e^{ix}\|_{L^{1}}$ does not converge to $0$ when $k\rightarrow\infty$?

Does an integral operator from $L^2$ to $L^2$ necessarily have a square integrable kernel?

Trending Questions

Popular # Hahtags

Popular Questions