Question

Looking for a bounded continuous $o(1)$ function on $]0, +\infty[$ that is not in $L^{p}(]0, +\infty[)$ for all $0 < p < +\infty$

score 73 · Answer 1 · 2016-11-10 11:13:57

73

Views

Looking for a bounded continuous $o(1)$ function on $]0, +\infty[$ that is not in $L^{p}(]0, +\infty[)$ for all $0 < p < +\infty$

Published on 10 Nov 2016 - 11:13

score 2.8k · Answer 2 · 2016-11-11 08:58:57

2.8k

Views

if $\int fg=0$ for all continuous function $g$ then $f=0$ a.e

Published on 11 Nov 2016 - 8:58

score 953 · Answer 3 · 2016-11-11 15:26:32

953

Views

Give an example of a function that satisfies strict inequality in Fatou's lemma and ....

Published on 11 Nov 2016 - 15:26

score 288 · Answer 4 · 2016-11-12 21:32:07

288

Views

$f \in AC[a,b]$ and $g$ continuous, $f'=g$ almost everywhere

Published on 12 Nov 2016 - 21:32

score 70 · Answer 5 · 2026-03-25 06:06:20

70

Views

$||f||_p <\infty$ , then there exist a sequence of simple functions $\{g_n\}$ such that $||g_n-f||_p\to 0$?

Published on 25 Mar 2026 - 6:06

score 43 · Answer 6 · 2026-04-07 20:07:33

43

Views

how does changing the definition of lebesgue measure influence the theorem of lebesgue convergence?

Published on 07 Apr 2026 - 20:07

score 110 · Answer 7 · 2016-11-13 11:57:56

110

Views

$\lim_{n \to \infty} f(x-n)=\lim_{n \to \infty} f(x+n)=0$ for Lebesgue integrable $f$

Published on 13 Nov 2016 - 11:57

score 71 · Answer 8 · 2026-04-07 18:05:50

71

Views

$L^P$ spaces inequality

Published on 07 Apr 2026 - 18:05

score 120 · Answer 9 · 2026-03-31 11:56:24

120

Views

The estimate of the convergence speed of 2D Riemann - lebesgue lemma.

Published on 31 Mar 2026 - 11:56

score 522 · Answer 10 · 2026-02-23 11:59:35

522

Views

Absolutely continuous implies Lipschitz on compact subsets?

Published on 23 Feb 2026 - 11:59

score 308 · Answer 11 · 2016-11-15 15:15:20

308

Views

Tricky Lebesgue Dominated Convergence Question

Published on 15 Nov 2016 - 15:15

score 52 · Answer 12 · 2016-11-16 13:41:01

52

Views

finite-difference operator and scalar product in $L_{2}(a,b)$

Published on 16 Nov 2016 - 13:41

score 91 · Answer 13 · 2016-11-16 18:13:41

91

Views

If is measurable and $\leq ()\leq $ for $\in$, and if $\mu(E)<\infty$, then $a\mu(E)\leq \int_E fd\mu \leq b \mu(E)$.

Published on 16 Nov 2016 - 18:13

score 70 · Answer 14 · 2016-11-16 18:45:53

70

Views

Concluding that the Lebesgue measure of an open ball $B_r(0)$ is $\pi$r^2

Published on 16 Nov 2016 - 18:45

score 77 · Answer 15 · 2016-11-17 11:10:41

77

Views

Is this formula true

Published on 17 Nov 2016 - 11:10

List Question

Looking for a bounded continuous $o(1)$ function on $]0, +\infty[$ that is not in $L^{p}(]0, +\infty[)$ for all $0 < p < +\infty$

if $\int fg=0$ for all continuous function $g$ then $f=0$ a.e

Give an example of a function that satisfies strict inequality in Fatou's lemma and ....

$f \in AC[a,b]$ and $g$ continuous, $f'=g$ almost everywhere

$||f||_p <\infty$ , then there exist a sequence of simple functions $\{g_n\}$ such that $||g_n-f||_p\to 0$?

how does changing the definition of lebesgue measure influence the theorem of lebesgue convergence?

$\lim_{n \to \infty} f(x-n)=\lim_{n \to \infty} f(x+n)=0$ for Lebesgue integrable $f$

$L^P$ spaces inequality

The estimate of the convergence speed of 2D Riemann - lebesgue lemma.

Absolutely continuous implies Lipschitz on compact subsets?

Tricky Lebesgue Dominated Convergence Question

finite-difference operator and scalar product in $L_{2}(a,b)$

If is measurable and $\leq ()\leq $ for $\in$, and if $\mu(E)<\infty$, then $a\mu(E)\leq \int_E fd\mu \leq b \mu(E)$.

Concluding that the Lebesgue measure of an open ball $B_r(0)$ is $\pi$r^2

Is this formula true

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