Question

How to prove that the length function of a half-open interval is monotone?

score 38 · Answer 1 · 2026-04-12 22:08:11

38

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How to prove that the length function of a half-open interval is monotone?

Published on 12 Apr 2026 - 22:08

score 512 · Answer 2 · 2026-04-13 09:24:43

512

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How to prove the set of the points where two measrable funcitons equal measurable?

Published on 13 Apr 2026 - 9:24

score 75 · Answer 3 · 2020-04-12 18:42:21

75

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norm of the functional $T(f)=\int_0^2f(x)dx-\int_3^{10}f(x)dx $ on $ L^2[0,10]$

Published on 12 Apr 2020 - 18:42

score 104 · Answer 4 · 2026-04-11 06:32:35

104

Views

Smallest Lebesgue measure and irrational number

Published on 11 Apr 2026 - 6:32

score 352 · Answer 5 · 2026-04-08 20:56:17

352

Views

Show that $E$ is Lebesgue measurable and $m(E)=0$

Published on 08 Apr 2026 - 20:56

score 65 · Answer 6 · 2026-04-12 02:35:20

65

Views

Differentiation of an integral (Lebesgue diffentiation theorem)

Published on 12 Apr 2026 - 2:35

score 279 · Answer 7 · 2026-04-12 23:36:33

279

Views

Infinite product Lebesgue measure as the pushforward of 1-Lebesgue measure

Published on 12 Apr 2026 - 23:36

score 293 · Answer 8 · 2026-04-08 20:59:32

293

Views

Proof that a closed set is measurable in "Measure and Integral" by Wheeden and Zygmund (Theorem 3.14)

Published on 08 Apr 2026 - 20:59

score 76 · Answer 9 · 2026-04-05 14:02:44

76

Views

$f,g \in L^3$ to prove $|f|=g$ a.e.

Published on 05 Apr 2026 - 14:02

score 377 · Answer 10 · 2026-04-12 01:35:02

377

Views

How to prove that the length function is countably additive?

Published on 12 Apr 2026 - 1:35

score 767 · Answer 11 · 2026-04-05 17:03:03

767

Views

Is there a set $A \subset [0,1]$ such that $\int_{A \times A^\text{c}} \frac{\mathrm{d} x \, \mathrm{d} y}{\lvert x - y\vert}=\infty$?

Published on 05 Apr 2026 - 17:03

score 46 · Answer 12 · 2020-04-16 02:31:19

Does is hold that $f \ge 0$ almost everywhere if $\int_a^b f \varphi dx = 0$ for all $\varphi \in C^\infty_0((a,b); [0,1])$?

score 356 · Answer 13 · 2026-04-05 17:01:54

356

Views

I need to prove that A is Lebesgue-measurable

Published on 05 Apr 2026 - 17:01

score 611 · Answer 14 · 2026-04-11 08:56:47

611

Views

Measure Theory problem about rectangle cover.

Published on 11 Apr 2026 - 8:56

score 274 · Answer 15 · 2026-04-13 10:29:49

274

Views

Integral of function equals integral of measure - Tonelli's Theorem

Published on 13 Apr 2026 - 10:29

List Question

How to prove that the length function of a half-open interval is monotone?

How to prove the set of the points where two measrable funcitons equal measurable?

norm of the functional $T(f)=\int_0^2f(x)dx-\int_3^{10}f(x)dx $ on $ L^2[0,10]$

Smallest Lebesgue measure and irrational number

Show that $E$ is Lebesgue measurable and $m(E)=0$

Differentiation of an integral (Lebesgue diffentiation theorem)

Infinite product Lebesgue measure as the pushforward of 1-Lebesgue measure

Proof that a closed set is measurable in "Measure and Integral" by Wheeden and Zygmund (Theorem 3.14)

$f,g \in L^3$ to prove $|f|=g$ a.e.

How to prove that the length function is countably additive?

Is there a set $A \subset [0,1]$ such that $\int_{A \times A^\text{c}} \frac{\mathrm{d} x \, \mathrm{d} y}{\lvert x - y\vert}=\infty$?

Does is hold that $f \ge 0$ almost everywhere if $\int_a^b f \varphi dx = 0$ for all $\varphi \in C^\infty_0((a,b); [0,1])$?

I need to prove that A is Lebesgue-measurable

Measure Theory problem about rectangle cover.

Integral of function equals integral of measure - Tonelli's Theorem

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