List questions from lp-spaces

Published on 01 Feb 2019 - 17:13

502

Views

Show that $e^{X^2/2} \in L^1$ iff $e^{XY} \in L^1$ iff $e^{|XY|} \in L^1$

Published on 29 Mar 2026 - 3:27

448

Views

Approximating the Lebesgue measure on the full real line with discrete measures

Published on 02 Feb 2019 - 23:48

456

Views

Showing that an integral operator on $L^p$ spaces has a certain norm

Published on 25 Mar 2026 - 4:57

212

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Do weak convergence and convergence of norms imply convergence in $L^1$?

Published on 28 Mar 2026 - 9:34

55

Views

Verification of convergence of random variables

Published on 28 Mar 2026 - 22:27

65

Views

Approximation of piecewise linear functions by constant function

Published on 25 Mar 2026 - 3:24

593

Views

S is a dense subset of $L^{p'}$, $\int_{E}fg = 0$ for all $f \in S$, then $g= 0$

Published on 05 Feb 2019 - 1:30

315

Views

$L^1$ convergent subsequence of increasing functions uniformly bounded in $L^2$

Published on 05 Feb 2019 - 10:19

53

Views

Generalisation: isomorphism of sequences spaces

Published on 25 Mar 2026 - 12:46

66

Views

Non compacity of a subset of $\ell^1$

Published on 05 Feb 2019 - 18:00

378

Views

$L^{q,\infty}(\mu) \subset L^p(\mu)$ with $1 \leq p<q <\infty$ and $\mu$ finite measure?

Published on 23 Mar 2026 - 7:10

104

Views

Problem on property of sequences of functions in Lp spaces

Published on 29 Mar 2026 - 2:54

43

Views

Determine $\varphi_{\epsilon}$

Published on 06 Feb 2019 - 10:44

52

Views

Upper estimate for an integral in norms

Published on 27 Mar 2026 - 0:02

List Question

Determine the LP spaces that contain a given function

Show that $e^{X^2/2} \in L^1$ iff $e^{XY} \in L^1$ iff $e^{|XY|} \in L^1$

Approximating the Lebesgue measure on the full real line with discrete measures

Showing that an integral operator on $L^p$ spaces has a certain norm

Do weak convergence and convergence of norms imply convergence in $L^1$?

Verification of convergence of random variables

Approximation of piecewise linear functions by constant function

S is a dense subset of $L^{p'}$, $\int_{E}fg = 0$ for all $f \in S$, then $g= 0$

$L^1$ convergent subsequence of increasing functions uniformly bounded in $L^2$

Generalisation: isomorphism of sequences spaces

Non compacity of a subset of $\ell^1$

$L^{q,\infty}(\mu) \subset L^p(\mu)$ with $1 \leq p<q <\infty$ and $\mu$ finite measure?

Problem on property of sequences of functions in Lp spaces

Determine $\varphi_{\epsilon}$

Upper estimate for an integral in norms

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