List questions from lp-spaces

Published on 28 Mar 2026 - 15:55

198

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If $f_{n}\rightharpoonup \bar{f}$ and $f_{n}(x) \rightarrow f(x)$ pointwise a.e., then is $\bar{f} = f$ a.e.?

Published on 15 Jul 2014 - 20:35

256

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Convergence of Step Function Defined by Averages

Published on 15 Jul 2014 - 23:37

23k

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Dual of $l^\infty$ is not $l^1$

Published on 26 Mar 2026 - 12:07

2k

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The dual space of locally integrable function space

Published on 16 Jul 2014 - 14:38

365

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Can we expect, $S(\mathbb R)\ast L^{p}(\mathbb R) \subset L^{p}(\mathbb R), (1<p<\infty) $?

Published on 26 Mar 2026 - 17:52

3.9k

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Reflexivity of $\ell^p$

Published on 31 Mar 2026 - 15:50

1.4k

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Not a basis for $ l^\infty$ then what is it?

Published on 31 Mar 2026 - 15:50

1.5k

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Weak-star lower semicontinuity in $L^\infty$

Published on 30 Mar 2026 - 6:46

107

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$L^\infty(\Omega)$ space

Published on 01 Apr 2026 - 8:02

358

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Fast Convergence of marginal distribtution

Published on 30 Mar 2026 - 6:46

77

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Given $u \in L^1$, is there approximating sequence $u_n \in L^\infty$ uniformly bounded in $L^p$?

Published on 26 Mar 2026 - 1:15

114

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$\|\phi_{\lambda}- \phi_{\lambda} \ast f \|_{L^{2}(\mathbb R)}\to 0$ as $\lambda \to \infty$? ($\phi_{\lambda}(x)=\lambda^{-1} \phi(x/\lambda).$)

Published on 19 Jul 2014 - 12:28

141

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On finite measurable space $X$, the whole of $L^p(X)$ is closed in $L^1(X)$ iff there is a const $C$ st $||f||_p\leq C||f||_1, \forall f \in L^p(X)$

Published on 19 Jul 2014 - 13:41

46

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$L^p$ integral on every measurable subset of $\Bbb R$

Published on 19 Jul 2014 - 19:31

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How to prove $\gamma$ is continuous?

If $f_{n}\rightharpoonup \bar{f}$ and $f_{n}(x) \rightarrow f(x)$ pointwise a.e., then is $\bar{f} = f$ a.e.?

Convergence of Step Function Defined by Averages

Dual of $l^\infty$ is not $l^1$

The dual space of locally integrable function space

Can we expect, $S(\mathbb R)\ast L^{p}(\mathbb R) \subset L^{p}(\mathbb R), (1<p<\infty) $?

Reflexivity of $\ell^p$

Not a basis for $ l^\infty$ then what is it?

Weak-star lower semicontinuity in $L^\infty$

$L^\infty(\Omega)$ space

Fast Convergence of marginal distribtution

Given $u \in L^1$, is there approximating sequence $u_n \in L^\infty$ uniformly bounded in $L^p$?

$\|\phi_{\lambda}- \phi_{\lambda} \ast f \|_{L^{2}(\mathbb R)}\to 0$ as $\lambda \to \infty$? ($\phi_{\lambda}(x)=\lambda^{-1} \phi(x/\lambda).$)

On finite measurable space $X$, the whole of $L^p(X)$ is closed in $L^1(X)$ iff there is a const $C$ st $||f||_p\leq C||f||_1, \forall f \in L^p(X)$

$L^p$ integral on every measurable subset of $\Bbb R$

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