Question

Is $\frac{\sin{x}}{x}\in L^1[\pi,\infty]$?

score 1.3k · Answer 1 · 2026-04-13 20:09:07

1.3k

Views

Is $\frac{\sin{x}}{x}\in L^1[\pi,\infty]$?

Published on 13 Apr 2026 - 20:09

score 571 · Answer 2 · 2026-04-13 21:27:54

571

Views

"Intermediate value theorem" for Lebesgue integrals and subsets

Published on 13 Apr 2026 - 21:27

score 874 · Answer 3 · 2026-04-14 06:38:43

874

Views

Using Lebesgue Dominated Convergence Theorem to prove Fatou's Lemma

Published on 14 Apr 2026 - 6:38

score 66 · Answer 4 · 2026-04-17 03:33:27

66

Views

Measurable functions such that $\int\underline{\text{lim}}f_n=0 $ and $\underline{\text{lim}}\int f_n=+\infty$.

Published on 17 Apr 2026 - 3:33

score 58 · Answer 5 · 2026-04-13 05:47:29

58

Views

Differentiating the expectated area under stochastic process

Published on 13 Apr 2026 - 5:47

score 75 · Answer 6 · 2026-04-12 05:49:15

75

Views

Hardy inequality punctured space

Published on 12 Apr 2026 - 5:49

score 156 · Answer 7 · 2026-04-15 20:57:30

156

Views

Showing $\left(\sum_1^\infty 2^{-n} \mathbf{1}_{x\in(0,1)}(x-r_n)^{-1/2}\right)^2$ is not integrable

Published on 15 Apr 2026 - 20:57

score 90 · Answer 8 · 2026-04-16 12:58:06

90

Views

$f$ be Lebesgue integrable and $F = m\{f > \alpha\}$, then $F$ is right continuous

Published on 16 Apr 2026 - 12:58

score 35 · Answer 9 · 2026-04-11 20:40:22

35

Views

Is this Integral transformation correct?

Published on 11 Apr 2026 - 20:40

score 149 · Answer 10 · 2026-04-09 04:38:46

149

Views

Proof of a double series equality

Published on 09 Apr 2026 - 4:38

score 155 · Answer 11 · 2026-04-15 18:00:02

155

Views

If $|\int f_n-\int f |\to 0 \Rightarrow\int |f_n - f| \to 0$.?

Published on 15 Apr 2026 - 18:00

score 119 · Answer 12 · 2026-04-17 08:09:08

119

Views

Exist $g:\mathbb{R}\to \mathbb{R}$ Lebesgue measurable and $h:[0, 1]\to \mathbb{R}$ Borel measurable such that $f = g \circ{}h$.

Published on 17 Apr 2026 - 8:09

score 3.5k · Answer 13 · 2026-04-09 05:27:22

3.5k

Views

Problem about limit of Lebesgue integral over a measurable set

Published on 09 Apr 2026 - 5:27

score 510 · Answer 14 · 2026-04-15 15:28:21

510

Views

a function that is not measurable but its square is measurable

Published on 15 Apr 2026 - 15:28

score 899 · Answer 15 · 2026-04-15 04:41:12

899

Views

Convergence of functions in $L^1$ implies convergence of derivatives $ a.e. $?

Published on 15 Apr 2026 - 4:41

List Question

Is $\frac{\sin{x}}{x}\in L^1[\pi,\infty]$?

"Intermediate value theorem" for Lebesgue integrals and subsets

Using Lebesgue Dominated Convergence Theorem to prove Fatou's Lemma

Measurable functions such that $\int\underline{\text{lim}}f_n=0 $ and $\underline{\text{lim}}\int f_n=+\infty$.

Differentiating the expectated area under stochastic process

Hardy inequality punctured space

Showing $\left(\sum_1^\infty 2^{-n} \mathbf{1}_{x\in(0,1)}(x-r_n)^{-1/2}\right)^2$ is not integrable

$f$ be Lebesgue integrable and $F = m\{f > \alpha\}$, then $F$ is right continuous

Is this Integral transformation correct?

Proof of a double series equality

If $|\int f_n-\int f |\to 0 \Rightarrow\int |f_n - f| \to 0$.?

Exist $g:\mathbb{R}\to \mathbb{R}$ Lebesgue measurable and $h:[0, 1]\to \mathbb{R}$ Borel measurable such that $f = g \circ{}h$.

Problem about limit of Lebesgue integral over a measurable set

a function that is not measurable but its square is measurable

Convergence of functions in $L^1$ implies convergence of derivatives $ a.e. $?

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