Question

Application of of Lebesgue integral properties in the scope of simple functions

score 263 · Answer 1 · 2026-04-12 07:58:45

263

Views

Application of of Lebesgue integral properties in the scope of simple functions

Published on 12 Apr 2026 - 7:58

score 53 · Answer 2 · 2026-04-17 15:25:49

53

Views

Upper bound Lebesgue measure of "square" of set on closed interval

Published on 17 Apr 2026 - 15:25

score 88 · Answer 3 · 2026-04-15 17:35:56

88

Views

Show $ f_n\xrightarrow{L^1}f\iff f_n\to f \text{ in measure} \iff f_n\to f \text{ almost uniformly} \iff f_n\to f \text{ a.e.}$

Published on 15 Apr 2026 - 17:35

score 82 · Answer 4 · 2026-04-11 17:00:55

82

Views

Weak convergence of a measure on a network to the Lebesgue measure

Published on 11 Apr 2026 - 17:00

score 154 · Answer 5 · 2026-04-14 21:28:03

154

Views

Show that the function $f(x)g(x)$ is integrable(2).

Published on 14 Apr 2026 - 21:28

score 54 · Answer 6 · 2026-04-16 18:06:28

54

Views

For any pair of sequences $(a_n),(b_n)$ with $a_n<b_n$ and $a_n \rightarrow \infty$ we have $\lim_n \int_{a_n}^{b_n} f d \mu=0$

Published on 16 Apr 2026 - 18:06

score 83 · Answer 7 · 2026-04-11 11:27:47

83

Views

Understanding the proof of Proposition 10 in Ch.2 in Real analysis by Royden and Fitzpatrick "Fourth Edition "

Published on 11 Apr 2026 - 11:27

score 128 · Answer 8 · 2026-04-12 16:36:33

128

Views

Does Lebesgue measurable set $E \subset [0,1]$ contain a $G_{\delta}$ set with the same measure?

Published on 12 Apr 2026 - 16:36

score 196 · Answer 9 · 2026-04-13 12:43:40

196

Views

Norm of Position Operator in $L^2[0,1]$

Published on 13 Apr 2026 - 12:43

score 239 · Answer 10 · 2026-04-11 10:00:25

239

Views

Characterisation of null sets (sets of measure zero) as divergences of sequences of step functions.

Published on 11 Apr 2026 - 10:00

score 38 · Answer 11 · 2026-03-26 02:57:52

38

Views

If $u \in L^2(0,T;L^2(\Omega))$ with $u(t) \in L^\infty(\Omega)$ uniformly, is $u \in L^\infty(0,T;L^\infty(\Omega))$?

Published on 26 Mar 2026 - 2:57

score 81 · Answer 12 · 2026-04-16 13:36:03

81

Views

$\lim_{n\to \infty}(\int_0^1 f(x)^{2n}g(x)^n h(x)~dx)^{1/n}$ where $f,g,h$ are positive continuous functions on $[0,1]$

Published on 16 Apr 2026 - 13:36

score 174 · Answer 13 · 2026-04-12 21:03:49

174

Views

Understanding the usage of lemma 16 on pg.47 (in Royden "Real analysis") in solving a problem.

Published on 12 Apr 2026 - 21:03

score 107 · Answer 14 · 2026-04-12 19:46:26

107

Views

Convergence in measure of $\cos(\frac{x}{n})$ for $x\in[0,\pi]$.

Published on 12 Apr 2026 - 19:46

score 648 · Answer 15 · 2026-04-11 09:32:31

648

Views

Approximation Lebesgue integral

Published on 11 Apr 2026 - 9:32

List Question

Application of of Lebesgue integral properties in the scope of simple functions

Upper bound Lebesgue measure of "square" of set on closed interval

Show $ f_n\xrightarrow{L^1}f\iff f_n\to f \text{ in measure} \iff f_n\to f \text{ almost uniformly} \iff f_n\to f \text{ a.e.}$

Weak convergence of a measure on a network to the Lebesgue measure

Show that the function $f(x)g(x)$ is integrable(2).

For any pair of sequences $(a_n),(b_n)$ with $a_n<b_n$ and $a_n \rightarrow \infty$ we have $\lim_n \int_{a_n}^{b_n} f d \mu=0$

Understanding the proof of Proposition 10 in Ch.2 in Real analysis by Royden and Fitzpatrick "Fourth Edition "

Does Lebesgue measurable set $E \subset [0,1]$ contain a $G_{\delta}$ set with the same measure?

Norm of Position Operator in $L^2[0,1]$

Characterisation of null sets (sets of measure zero) as divergences of sequences of step functions.

If $u \in L^2(0,T;L^2(\Omega))$ with $u(t) \in L^\infty(\Omega)$ uniformly, is $u \in L^\infty(0,T;L^\infty(\Omega))$?

$\lim_{n\to \infty}(\int_0^1 f(x)^{2n}g(x)^n h(x)~dx)^{1/n}$ where $f,g,h$ are positive continuous functions on $[0,1]$

Understanding the usage of lemma 16 on pg.47 (in Royden "Real analysis") in solving a problem.

Convergence in measure of $\cos(\frac{x}{n})$ for $x\in[0,\pi]$.

Approximation Lebesgue integral

Trending Questions

Popular # Hahtags

Popular Questions