Question

Where $\{q_n\}=\mathbb Q$ and $f_n:[q_n-2^{-n-1},q_n+2^{-n-1}]\to[0,\infty)$ with $\int f_n\,d\lambda=1$, show $\sum_{n=1}^\infty f_n<\infty$ a.e.

score 1.5k · Answer 1 · 2026-04-17 01:48:23

1.5k

Views

Where $\{q_n\}=\mathbb Q$ and $f_n:[q_n-2^{-n-1},q_n+2^{-n-1}]\to[0,\infty)$ with $\int f_n\,d\lambda=1$, show $\sum_{n=1}^\infty f_n<\infty$ a.e.

Published on 17 Apr 2026 - 1:48

score 921 · Answer 2 · 2026-03-28 01:25:59

921

Views

Different approaches to differentiability in $L^2$

Published on 28 Mar 2026 - 1:25

score 160 · Answer 3 · 2026-04-12 21:20:10

160

Views

Bound on integrable nonnegative function $F$ given inequality with compactly supported continuous functions.

Published on 12 Apr 2026 - 21:20

score 49 · Answer 4 · 2026-04-15 06:54:29

49

Views

Well-definedness of Fourier transform of $f\in L^1(\mathbb{R})$

Published on 15 Apr 2026 - 6:54

score 110 · Answer 5 · 2026-04-14 04:14:24

110

Views

Differentiation under the integral sign, where the partial derivative of the integrand is not bounded by a Lebesgue integrable function.

Published on 14 Apr 2026 - 4:14

score 241 · Answer 6 · 2026-04-16 12:26:10

241

Views

$L^p \subset L^q$

Published on 16 Apr 2026 - 12:26

score 144 · Answer 7 · 2026-04-12 10:53:51

144

Views

Frullani's theorem in complex context, other examples

Published on 12 Apr 2026 - 10:53

score 82 · Answer 8 · 2026-04-10 05:15:47

82

Views

On sharp bounds of some dyadic operators

Published on 10 Apr 2026 - 5:15

score 92 · Answer 9 · 2026-04-12 23:58:20

92

Views

Lebesgue integral of $\frac{1}{\|\boldsymbol{x}-\boldsymbol{r}\|^2}$ on an infinite cylinder

Published on 12 Apr 2026 - 23:58

score 533 · Answer 10 · 2026-04-13 04:14:07

533

Views

Is it correct to interpret the "dx" in the standard notation for integrals as the Lebesgue measure?

Published on 13 Apr 2026 - 4:14

score 84 · Answer 11 · 2026-04-21 09:08:45

84

Views

Bounding $L_p$ norms on a convergent $L_1$ sequence

Published on 21 Apr 2026 - 9:08

score 181 · Answer 12 · 2026-03-30 23:30:44

181

Views

How can I solve this triple integral $\iiint_{B} y\;dxdydz$ on a defined set?

Published on 30 Mar 2026 - 23:30

score 63 · Answer 13 · 2026-03-30 17:38:09

63

Views

How can I find the measure of $B=\{(x,y,z) \in\mathbb R^3| \; x^2+y^2+4z^2 \le3, \;x^2-y^2+4z^2\le1, \; z\ge 0\}$?

Published on 30 Mar 2026 - 17:38

score 185 · Answer 14 · 2026-04-10 17:37:28

185

Views

How to start an eigenvalue problem

Published on 10 Apr 2026 - 17:37

score 147 · Answer 15 · 2026-04-16 20:23:38

147

Views

If $\{f_n\}\subset L_1([0,1])$, $f_n\to f$ pointwise, and $\sup_{n} \int_{0}^{1} |f_n|\max (0, \log |f_n|)<\infty$, then $f_n\to f$ in $L_1$

Published on 16 Apr 2026 - 20:23

List Question

Where $\{q_n\}=\mathbb Q$ and $f_n:[q_n-2^{-n-1},q_n+2^{-n-1}]\to[0,\infty)$ with $\int f_n\,d\lambda=1$, show $\sum_{n=1}^\infty f_n<\infty$ a.e.

Different approaches to differentiability in $L^2$

Bound on integrable nonnegative function $F$ given inequality with compactly supported continuous functions.

Well-definedness of Fourier transform of $f\in L^1(\mathbb{R})$

Differentiation under the integral sign, where the partial derivative of the integrand is not bounded by a Lebesgue integrable function.

$L^p \subset L^q$

Frullani's theorem in complex context, other examples

On sharp bounds of some dyadic operators

Lebesgue integral of $\frac{1}{\|\boldsymbol{x}-\boldsymbol{r}\|^2}$ on an infinite cylinder

Is it correct to interpret the "dx" in the standard notation for integrals as the Lebesgue measure?

Bounding $L_p$ norms on a convergent $L_1$ sequence

How can I solve this triple integral $\iiint_{B} y\;dxdydz$ on a defined set?

How can I find the measure of $B=\{(x,y,z) \in\mathbb R^3| \; x^2+y^2+4z^2 \le3, \;x^2-y^2+4z^2\le1, \; z\ge 0\}$?

How to start an eigenvalue problem

If $\{f_n\}\subset L_1([0,1])$, $f_n\to f$ pointwise, and $\sup_{n} \int_{0}^{1} |f_n|\max (0, \log |f_n|)<\infty$, then $f_n\to f$ in $L_1$

Trending Questions

Popular # Hahtags

Popular Questions