List questions from lp-spaces

107

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How does one prove that partial functions of measurable functions of 2 var. are nearly all measurable?

Published on 29 Mar 2026 - 20:05

125

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Prove that Fourier basis is maximal orthonormal set in real L2

Published on 08 Apr 2026 - 6:11

77

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Brezis' exercise 4.14: Vitali theorem

Published on 04 Apr 2023 - 20:42

199

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A hint in Brezis' exercise 4.16.1

Published on 07 Apr 2026 - 6:30

154

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Brezis' exercise 4.16.1

Published on 06 Apr 2026 - 0:56

77

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Brezis' exercise 4.16.2

Published on 26 Mar 2026 - 3:19

169

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Show that $X$ is finite and $E(|X|)<\infty$

Published on 26 Mar 2026 - 11:03

31

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Definition of a certain discrete $L^p$ space?

Published on 05 Apr 2023 - 15:19

69

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Brezis' exercise 4.16.3

Published on 26 Mar 2026 - 6:20

79

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The span of the space of characteristic functions of open bounded intervals is dense in $L^p (\mathbb R)$ for $p \in [1, \infty)$

Published on 06 Apr 2023 - 15:50

28

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$u_n \to \overline f$ in the weak topology $\sigma(L^p, L^{p'})$

Published on 26 Mar 2026 - 4:53

182

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Is it necessary to consider the case $p=1$ separately?

Published on 26 Mar 2026 - 4:50

47

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Compute $\lim_n \|u_n-\bar f\|_p$

Published on 31 Mar 2026 - 19:12

97

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Alternative proofs of $L^q[0,1]$ is a (Baire) first category subset in $L^p[0,1]$

Published on 29 Mar 2026 - 13:47

102

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An example of $(f_n)$ such that $f_n \to f$ in $\sigma(L^1, L^\infty)$ and $\|f_n\|_1 \to \|f\|_1$, but $\|f_n-f\|_1 \not \to 0$

Published on 06 Apr 2026 - 14:21

List Question

How does one prove that partial functions of measurable functions of 2 var. are nearly all measurable?

Prove that Fourier basis is maximal orthonormal set in real L2

Brezis' exercise 4.14: Vitali theorem

A hint in Brezis' exercise 4.16.1

Brezis' exercise 4.16.1

Brezis' exercise 4.16.2

Show that $X$ is finite and $E(|X|)<\infty$

Definition of a certain discrete $L^p$ space?

Brezis' exercise 4.16.3

The span of the space of characteristic functions of open bounded intervals is dense in $L^p (\mathbb R)$ for $p \in [1, \infty)$

$u_n \to \overline f$ in the weak topology $\sigma(L^p, L^{p'})$

Is it necessary to consider the case $p=1$ separately?

Compute $\lim_n \|u_n-\bar f\|_p$

Alternative proofs of $L^q[0,1]$ is a (Baire) first category subset in $L^p[0,1]$

An example of $(f_n)$ such that $f_n \to f$ in $\sigma(L^1, L^\infty)$ and $\|f_n\|_1 \to \|f\|_1$, but $\|f_n-f\|_1 \not \to 0$

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