List questions from lp-spaces

Published on 15 Apr 2026 - 23:05

138

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Proof of converse of Young's convolution inequality

Published on 10 May 2026 - 17:38

202

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Question regarding $\mathscr L^\infty$ and an exercise in Cohn's textbook

Published on 16 Apr 2026 - 15:20

120

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normalized arc length measure

Published on 13 Apr 2026 - 7:44

120

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On Bartle's 'Elements of Integration' Exercise 7.T

Published on 17 Apr 2026 - 13:36

184

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On Bartle's 'Elements of Integration' Exercise 7.U

Published on 22 Apr 2026 - 6:54

35

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$L^p$ spaces inclusions

Published on 13 Apr 2026 - 14:59

251

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Composition of continuous and $L^p$ function is in $L^p$

Published on 12 Apr 2026 - 5:49

59

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For any $\varepsilon>0$ there is measurable set $E$ with $\mu(E)<\infty$ such that $|f(x)|<\varepsilon$ on $E$

Published on 13 Apr 2026 - 21:41

109

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Proving $M_n := e^{S_n - n/2}$ does not converge in $L^2$

Published on 17 Apr 2026 - 18:00

42

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Convergence in mean with additional hypothesis implies convergence in measure

Published on 11 Apr 2026 - 4:56

212

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Does a $L_1$-bounded sequence of $L_1$ functions has a subsequence that converges to a finite measure as a sequence of measures?

Published on 14 Apr 2026 - 18:30

36

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If $L^\infty(X;\mu)$ is separable, then it is finite dimensional

Published on 16 Apr 2026 - 0:27

83

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Proving $L^1$ is complete, why is a subsequence necessary?

Published on 14 Apr 2026 - 6:42

49

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Let $H, H_n \in L_p^*$ such that $H_n (f) := H(f1_{X_n})$ for all $f \in L_p$. Are there some relations between $H, H_n$?

Published on 11 Apr 2026 - 16:27

List Question

Embedding $L^1 [0,1]\subseteq \bigcup_{p>1} L^p[0,1]$

Proof of converse of Young's convolution inequality

Question regarding $\mathscr L^\infty$ and an exercise in Cohn's textbook

normalized arc length measure

On Bartle's 'Elements of Integration' Exercise 7.T

On Bartle's 'Elements of Integration' Exercise 7.U

$L^p$ spaces inclusions

Composition of continuous and $L^p$ function is in $L^p$

For any $\varepsilon>0$ there is measurable set $E$ with $\mu(E)<\infty$ such that $|f(x)|<\varepsilon$ on $E$

Proving $M_n := e^{S_n - n/2}$ does not converge in $L^2$

Convergence in mean with additional hypothesis implies convergence in measure

Does a $L_1$-bounded sequence of $L_1$ functions has a subsequence that converges to a finite measure as a sequence of measures?

If $L^\infty(X;\mu)$ is separable, then it is finite dimensional

Proving $L^1$ is complete, why is a subsequence necessary?

Let $H, H_n \in L_p^*$ such that $H_n (f) := H(f1_{X_n})$ for all $f \in L_p$. Are there some relations between $H, H_n$?

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