Question

$\int_{[a,b]}f\, dm>0$ for all interval $[a,b]$ implies $f>0$ almost everywhere

score 90 · Answer 1 · 2026-04-15 19:01:03

90

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$\int_{[a,b]}f\, dm>0$ for all interval $[a,b]$ implies $f>0$ almost everywhere

Published on 15 Apr 2026 - 19:01

score 164 · Answer 2 · 2026-04-16 01:30:54

164

Views

For all $\epsilon >0$ ,exists $\delta>0$ such that if $||t||<\delta$ then: $ \int_{\mathbb{R^d}} |f(x-t)-f(x)| \,dx< \epsilon $

Published on 16 Apr 2026 - 1:30

score 46 · Answer 3 · 2026-04-15 08:25:07

46

Views

Product measure over a collection of sets.

Published on 15 Apr 2026 - 8:25

score 73 · Answer 4 · 2026-04-17 02:51:09

73

Views

$f \in L^1 $, does that imply $f(\lfloor x \rfloor) \in L^1$?

Published on 17 Apr 2026 - 2:51

score 283 · Answer 5 · 2026-04-11 06:37:20

283

Views

last step in gamma function derivation using dominated converge theorem

Published on 11 Apr 2026 - 6:37

score 357 · Answer 6 · 2026-04-14 18:00:19

357

Views

Associativity of the Lebesgue-Stieltjes integral

Published on 14 Apr 2026 - 18:00

score 163 · Answer 7 · 2026-04-12 23:42:06

163

Views

prove that $\chi_{(0,1)} - \chi_{S}$ is not a limit of increasing step functions.

Published on 12 Apr 2026 - 23:42

score 71 · Answer 8 · 2026-04-16 04:55:06

71

Views

Proving the existence of the limit of $f^2$ when $(f^2)^{'}$ belongs to $L_{2}(0,\infty)$

Published on 16 Apr 2026 - 4:55

score 522 · Answer 9 · 2026-04-10 23:06:32

522

Views

Interchange of summation of measures and integral

Published on 10 Apr 2026 - 23:06

score 156 · Answer 10 · 2026-04-10 09:21:18

156

Views

Finding the limit of a lebesgue integral

Published on 10 Apr 2026 - 9:21

score 128 · Answer 11 · 2026-04-15 07:03:34

128

Views

A kind of Tauberian theorem for $L^2(\mathbb R^n)$?

Published on 15 Apr 2026 - 7:03

score 247 · Answer 12 · 2026-04-09 20:49:19

247

Views

Forming a triangle out of 3 rods

Published on 09 Apr 2026 - 20:49

score 92 · Answer 13 · 2026-03-26 17:46:17

92

Views

Bochner integral of a function in $L^2$

Published on 26 Mar 2026 - 17:46

score 168 · Answer 14 · 2026-05-11 01:54:41

168

Views

If $μ$ is a signed measure, $Ω^±$ is a Hahn decomposition and $μ^±$ is the Jordan decomposition, then $\int_{A∩Ω^±}X{\rm d}μ=\pm\int_AX{\rm d}μ^±$

Published on 11 May 2026 - 1:54

score 43 · Answer 15 · 2026-04-16 05:50:42

$ \frac{\partial}{\partial x_i} \int_{\mathbb{R^d}} f(x_0,y)\, dy = \int_{\mathbb{R^d}} \frac{\partial}{\partial x_i} f(x_0,y)\, dy $

List Question

$\int_{[a,b]}f\, dm>0$ for all interval $[a,b]$ implies $f>0$ almost everywhere

For all $\epsilon >0$ ,exists $\delta>0$ such that if $||t||<\delta$ then: $ \int_{\mathbb{R^d}} |f(x-t)-f(x)| \,dx< \epsilon $

Product measure over a collection of sets.

$f \in L^1 $, does that imply $f(\lfloor x \rfloor) \in L^1$?

last step in gamma function derivation using dominated converge theorem

Associativity of the Lebesgue-Stieltjes integral

prove that $\chi_{(0,1)} - \chi_{S}$ is not a limit of increasing step functions.

Proving the existence of the limit of $f^2$ when $(f^2)^{'}$ belongs to $L_{2}(0,\infty)$

Interchange of summation of measures and integral

Finding the limit of a lebesgue integral

A kind of Tauberian theorem for $L^2(\mathbb R^n)$?

Forming a triangle out of 3 rods

Bochner integral of a function in $L^2$

If $μ$ is a signed measure, $Ω^±$ is a Hahn decomposition and $μ^±$ is the Jordan decomposition, then $\int_{A∩Ω^±}X{\rm d}μ=\pm\int_AX{\rm d}μ^±$

$ \frac{\partial}{\partial x_i} \int_{\mathbb{R^d}} f(x_0,y)\, dy = \int_{\mathbb{R^d}} \frac{\partial}{\partial x_i} f(x_0,y)\, dy $

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