List questions from bochner-spaces

Published on 25 Mar 2026 - 8:28

84

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If $\mu$ is a finite measure and $ν$ is a vector measure with $|\nu|\le C\mu$, are we able to show $\left|\frac{{\rm d}ν}{{\rm d}\mu}\right|\le C$?

Published on 25 Mar 2026 - 8:04

143

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Density of simple functions in Bochner space; approximation from below

Published on 17 Mar 2026 - 16:03

43

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Does it make sense to define strongly measurable functions on a Polish space instead of a Banch space?

Published on 17 Mar 2026 - 13:46

1.2k

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Arzela-Ascoli-type embedding: Is $H^1(0,T;X)$ compactly embedded in $C([0,T];X)$?

Published on 22 Mar 2026 - 21:59

224

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Sequential Banach-Alaoglu theorem for a Bochner space

Published on 17 Mar 2026 - 5:31

254

Views

Compute the dual of the $L^1$ space of $L^1$-valued functions (Lebesgue-Bochner space)

Published on 25 Mar 2026 - 10:34

134

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Density of $C_c^\infty((0,T)\times R^d)$ in $L^2(0,T;H^1)$

Published on 17 Mar 2026 - 9:21

76

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Show that the integral of a two-parameter function is Hölder continuous

Published on 17 Mar 2026 - 3:20

492

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Weak continuity of functions with values in a Banach space

Published on 17 Mar 2026 - 10:10

116

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Weak limit in Bochner-Sobolev space

Published on 17 Mar 2026 - 3:22

97

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Boundedness of an operator on a Bochner spaces

Published on 25 Mar 2026 - 4:39

218

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Integration in normed vector spaces

Published on 22 Mar 2026 - 13:32

896

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Absolutely continuous and differentiable almost everywhere

Published on 22 Mar 2026 - 17:27

222

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The restriction of a variable in a Sobolev function is a.e. Sobolev

Published on 22 Mar 2026 - 3:46

List Question

Weak star convergence in $L^\infty(0,T;L^2(\Omega))$ and pointwise weak limits

If $\mu$ is a finite measure and $ν$ is a vector measure with $|\nu|\le C\mu$, are we able to show $\left|\frac{{\rm d}ν}{{\rm d}\mu}\right|\le C$?

Density of simple functions in Bochner space; approximation from below

Does it make sense to define strongly measurable functions on a Polish space instead of a Banch space?

Arzela-Ascoli-type embedding: Is $H^1(0,T;X)$ compactly embedded in $C([0,T];X)$?

Sequential Banach-Alaoglu theorem for a Bochner space

Compute the dual of the $L^1$ space of $L^1$-valued functions (Lebesgue-Bochner space)

Density of $C_c^\infty((0,T)\times R^d)$ in $L^2(0,T;H^1)$

Show that the integral of a two-parameter function is Hölder continuous

Weak continuity of functions with values in a Banach space

Weak limit in Bochner-Sobolev space

Boundedness of an operator on a Bochner spaces

Integration in normed vector spaces

Absolutely continuous and differentiable almost everywhere

The restriction of a variable in a Sobolev function is a.e. Sobolev

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