Question

Measure Theory on integrals

score 50 · Answer 1 · 2026-04-21 22:24:28

50

Views

Measure Theory on integrals

Published on 21 Apr 2026 - 22:24

score 97 · Answer 2 · 2026-04-15 17:36:11

97

Views

Show $\int_\pi^\infty \frac{dx}{x^2 \left( \sin^2(x) \right)^{1/3}}$ is finite using 1st semester measure theory

Published on 15 Apr 2026 - 17:36

score 1.3k · Answer 3 · 2026-04-13 20:14:47

1.3k

Views

Chebyshev's Inequality in proof of Proposition 23 of Royden?

Published on 13 Apr 2026 - 20:14

score 130 · Answer 4 · 2026-04-23 00:21:14

130

Views

Criterion for a signed measure to be positive

Published on 23 Apr 2026 - 0:21

score 85 · Answer 5 · 2026-04-13 08:42:04

85

Views

Will the integral still be 1?

Published on 13 Apr 2026 - 8:42

score 79 · Answer 6 · 2026-04-10 21:31:37

79

Views

Will the joint probability density exist in this case?

Published on 10 Apr 2026 - 21:31

score 224 · Answer 7 · 2026-04-14 02:21:00

224

Views

In the theorem of coincidence of $R$ and $L$ integrals: are we assuming the $\Bbb L$ $\sigma$-algebra? If not, how to prove the measurability of $f$?

Published on 14 Apr 2026 - 2:21

score 124 · Answer 8 · 2026-04-13 15:04:37

124

Views

Limit of integral over $[0,1]$ of $\frac{ne^{-x}}{1+nx}$

Published on 13 Apr 2026 - 15:04

score 142 · Answer 9 · 2026-04-11 13:37:40

142

Views

Limit of Lebesgue integral over an increment of a function

Published on 11 Apr 2026 - 13:37

score 161 · Answer 10 · 2026-04-15 14:46:53

161

Views

Show that the Lebesgue intergral $\int_{1}^{\infty} x^{-b} e^{\sin {x}} \sin {(2x)}\, dx$ exists iff $b>1$

Published on 15 Apr 2026 - 14:46

score 94 · Answer 11 · 2026-04-14 23:46:10

94

Views

Limit of the integral over $[0,n]$ of $(1-\frac{x}{n})^n e^{\frac{x}{2}}$

Published on 14 Apr 2026 - 23:46

score 302 · Answer 12 · 2026-04-14 08:19:45

302

Views

Riemann–Stieltjes integral of an indicator function

Published on 14 Apr 2026 - 8:19

score 109 · Answer 13 · 2026-04-21 22:46:14

109

Views

Which assumptions on $Ω\subseteq\mathbb R^d$ do we need in order to show density of $C_c^∞(Ω)$ in $(L^p(Ω),\left\|\;\cdot\;\right\|_{L^p(Ω)})$?

Published on 21 Apr 2026 - 22:46

score 44 · Answer 14 · 2026-04-21 23:00:01

44

Views

If $u\in L^p(\Omega;\mathbb R^d)$, then $u_i\in L^p(\Omega)$ for all $i\in\left\{1,\ldots,d\right\}$. Does the reverse hold true?

Published on 21 Apr 2026 - 23:00

score 337 · Answer 15 · 2026-04-13 14:29:36

337

Views

A very simple example of the dominated convergence theorem

Published on 13 Apr 2026 - 14:29

List Question

Measure Theory on integrals

Show $\int_\pi^\infty \frac{dx}{x^2 \left( \sin^2(x) \right)^{1/3}}$ is finite using 1st semester measure theory

Chebyshev's Inequality in proof of Proposition 23 of Royden?

Criterion for a signed measure to be positive

Will the integral still be 1?

Will the joint probability density exist in this case?

In the theorem of coincidence of $R$ and $L$ integrals: are we assuming the $\Bbb L$ $\sigma$-algebra? If not, how to prove the measurability of $f$?

Limit of integral over $[0,1]$ of $\frac{ne^{-x}}{1+nx}$

Limit of Lebesgue integral over an increment of a function

Show that the Lebesgue intergral $\int_{1}^{\infty} x^{-b} e^{\sin {x}} \sin {(2x)}\, dx$ exists iff $b>1$

Limit of the integral over $[0,n]$ of $(1-\frac{x}{n})^n e^{\frac{x}{2}}$

Riemann–Stieltjes integral of an indicator function

Which assumptions on $Ω\subseteq\mathbb R^d$ do we need in order to show density of $C_c^∞(Ω)$ in $(L^p(Ω),\left\|\;\cdot\;\right\|_{L^p(Ω)})$?

If $u\in L^p(\Omega;\mathbb R^d)$, then $u_i\in L^p(\Omega)$ for all $i\in\left\{1,\ldots,d\right\}$. Does the reverse hold true?

A very simple example of the dominated convergence theorem

Trending Questions

Popular # Hahtags

Popular Questions