Question

Lebesgue integrability of step functions

score 130 · Answer 1 · 2026-04-11 16:26:28

130

Views

Lebesgue integrability of step functions

Published on 11 Apr 2026 - 16:26

score 1k · Answer 2 · 2026-04-15 07:48:33

1k

Views

Is the function $f(x,y) = \frac{x^2 - y^2}{(x^2+y^2)^2}$ lebesgue integrable in $[0,1]\times[0,1]$?

Published on 15 Apr 2026 - 7:48

score 76 · Answer 3 · 2026-04-10 08:05:20

76

Views

Convergence in norm

Published on 10 Apr 2026 - 8:05

score 82 · Answer 4 · 2026-04-15 18:37:07

82

Views

Show that there is no Lebesgue integrable function $g$ satisfying $n\chi_{(0,\frac1n]}\leqslant g$ for all $n$.

Published on 15 Apr 2026 - 18:37

score 72 · Answer 5 · 2026-04-19 21:40:09

72

Views

$ \lVert {\bf f} \rVert_{p} \leqslant (m(E))^{1-1/p} \lVert {\bf f} \rVert_{\infty} $ for any $ f \in L_{\infty}(E) $

Published on 19 Apr 2026 - 21:40

score 85 · Answer 6 · 2026-03-27 14:55:16

85

Views

If given conditions are satisfied, then prove that $f$ is absolutely continuous on any interval $[a,b]$

Published on 27 Mar 2026 - 14:55

score 53 · Answer 7 · 2026-04-15 07:12:52

53

Views

Equivalence of these double integrals.

Published on 15 Apr 2026 - 7:12

score 464 · Answer 8 · 2026-04-16 09:05:58

464

Views

prove that $ \int_E f(x) dm \ge \delta$ whenever $m(E) \ge \epsilon$

Published on 16 Apr 2026 - 9:05

score 458 · Answer 9 · 2026-04-15 06:10:56

458

Views

Antiderivative $f(x)=\int_{a}^{x} g(x)$ is differentiable almost everywhere on (a,b)

Published on 15 Apr 2026 - 6:10

score 44 · Answer 10 · 2026-04-12 04:39:00

44

Views

Example of a Lebesgue integrable function under certain conditions

Published on 12 Apr 2026 - 4:39

score 928 · Answer 11 · 2026-04-13 21:36:42

928

Views

Use the definition of the integral to prove that if $A \subset E$, where $E$ is measurable, then $\int_A f = \int_E f \chi_{A}$

Published on 13 Apr 2026 - 21:36

score 499 · Answer 12 · 2026-03-27 14:49:24

499

Views

Difference of increasing functions differentiable a.e.

Published on 27 Mar 2026 - 14:49

score 1k · Answer 13 · 2026-04-09 00:57:34

1k

Views

Bounded variation and Integration

Published on 09 Apr 2026 - 0:57

score 928 · Answer 14 · 2015-11-16 21:59:08

928

Views

Problems with Proof of Jensen's Inequality (Durrett's "Probability Theory and Examples")

Published on 16 Nov 2015 - 21:59

score 336 · Answer 15 · 2015-11-16 22:07:39

336

Views

If $\int_A f\,dm = 0$ for all $A$ having some fixed measure $C$, then $f = 0$ almost everywhere

Published on 16 Nov 2015 - 22:07

List Question

Lebesgue integrability of step functions

Is the function $f(x,y) = \frac{x^2 - y^2}{(x^2+y^2)^2}$ lebesgue integrable in $[0,1]\times[0,1]$?

Convergence in norm

Show that there is no Lebesgue integrable function $g$ satisfying $n\chi_{(0,\frac1n]}\leqslant g$ for all $n$.

$ \lVert {\bf f} \rVert_{p} \leqslant (m(E))^{1-1/p} \lVert {\bf f} \rVert_{\infty} $ for any $ f \in L_{\infty}(E) $

If given conditions are satisfied, then prove that $f$ is absolutely continuous on any interval $[a,b]$

Equivalence of these double integrals.

prove that $ \int_E f(x) dm \ge \delta$ whenever $m(E) \ge \epsilon$

Antiderivative $f(x)=\int_{a}^{x} g(x)$ is differentiable almost everywhere on (a,b)

Example of a Lebesgue integrable function under certain conditions

Use the definition of the integral to prove that if $A \subset E$, where $E$ is measurable, then $\int_A f = \int_E f \chi_{A}$

Difference of increasing functions differentiable a.e.

Bounded variation and Integration

Problems with Proof of Jensen's Inequality (Durrett's "Probability Theory and Examples")

If $\int_A f\,dm = 0$ for all $A$ having some fixed measure $C$, then $f = 0$ almost everywhere

Trending Questions

Popular # Hahtags

Popular Questions