Question

How to prove that $\int_0^1 dx \int_0^x f(x,y) dy = \int_0^1 dy \int_y^1 f(x,y) dx$ for a continuous function $f$ the given interval

score 121 · Answer 1 · 2026-05-10 15:03:10

121

Views

How to prove that $\int_0^1 dx \int_0^x f(x,y) dy = \int_0^1 dy \int_y^1 f(x,y) dx$ for a continuous function $f$ the given interval

Published on 10 May 2026 - 15:03

score 136 · Answer 2 · 2026-05-07 09:06:55

136

Views

Is it true $\mu (A+B) = \mu (A) + \mu(B) $ for bounded sets $ A, B \subset R $

Published on 07 May 2026 - 9:06

score 204 · Answer 3 · 2026-04-17 09:20:49

204

Views

If $|E|=0$ then $f$ is measurable

Published on 17 Apr 2026 - 9:20

score 688 · Answer 4 · 2026-05-04 03:56:32

688

Views

For $E\subset\mathbb R^n$ with Lebesgue outer measure $0<m^(E)<\infty$, $\alpha\in(0,1)$, there is a ball $B$ with $m^(E\cap B)\ge \alpha m^*(B)$.

Published on 04 May 2026 - 3:56

score 58 · Answer 5 · 2026-04-30 16:58:26

58

Views

Lebesgue's monotone convergence theorem, - boundedness

Published on 30 Apr 2026 - 16:58

score 243 · Answer 6 · 2026-05-10 12:39:25

243

Views

Consider the operator $T:L^2(0,1)\rightarrow L^2(0,1)$. Is it well defined, linear, bounded, compact?

Published on 10 May 2026 - 12:39

score 1k · Answer 7 · 2026-05-03 16:13:19

1k

Views

Radon-Nikodym derivative of discrete measure

Published on 03 May 2026 - 16:13

score 222 · Answer 8 · 2026-04-10 23:20:01

222

Views

Borel set with constant positive but not full measure in each interval.

Published on 10 Apr 2026 - 23:20

score 45 · Answer 9 · 2026-05-10 12:34:23

45

Views

Prove that for any $k \in \Bbb{R}$ we have$ \quad \mu^{}(kA) = |k|\mu^{}A, $

Published on 10 May 2026 - 12:34

score 513 · Answer 10 · 2026-04-14 22:31:24

513

Views

Borel set with translation invariant measure in each interval of any length

Published on 14 Apr 2026 - 22:31

score 67 · Answer 11 · 2026-04-12 08:31:02

67

Views

A measure space which is not finite but implies $L^p$ inclusion

Published on 12 Apr 2026 - 8:31

score 60 · Answer 12 · 2026-04-13 20:51:03

60

Views

Sum of a zero-measure sets

Published on 13 Apr 2026 - 20:51

score 59 · Answer 13 · 2026-04-11 21:01:01

59

Views

Need for a set to have finite Lebesgue measure.

Published on 11 Apr 2026 - 21:01

score 381 · Answer 14 · 2026-04-13 20:22:38

381

Views

Length is a Pre-Measure on the Semi-Ring of Bounded Half-Open Real Intervals

Published on 13 Apr 2026 - 20:22

score 94 · Answer 15 · 2026-04-15 23:03:43

94

Views

Do all measure zero sets belong to the measure space: If $\mu(N_1) = 0$ then is $N_1 \in \mathcal{M}_{\mu}$?

Published on 15 Apr 2026 - 23:03

List Question

How to prove that $\int_0^1 dx \int_0^x f(x,y) dy = \int_0^1 dy \int_y^1 f(x,y) dx$ for a continuous function $f$ the given interval

Is it true $\mu (A+B) = \mu (A) + \mu(B) $ for bounded sets $ A, B \subset R $

If $|E|=0$ then $f$ is measurable

For $E\subset\mathbb R^n$ with Lebesgue outer measure $0<m^(E)<\infty$, $\alpha\in(0,1)$, there is a ball $B$ with $m^(E\cap B)\ge \alpha m^*(B)$.

Lebesgue's monotone convergence theorem, - boundedness

Consider the operator $T:L^2(0,1)\rightarrow L^2(0,1)$. Is it well defined, linear, bounded, compact?

Radon-Nikodym derivative of discrete measure

Borel set with constant positive but not full measure in each interval.

Prove that for any $k \in \Bbb{R}$ we have$ \quad \mu^{}(kA) = |k|\mu^{}A, $

Borel set with translation invariant measure in each interval of any length

A measure space which is not finite but implies $L^p$ inclusion

Sum of a zero-measure sets

Need for a set to have finite Lebesgue measure.

Length is a Pre-Measure on the Semi-Ring of Bounded Half-Open Real Intervals

Do all measure zero sets belong to the measure space: If $\mu(N_1) = 0$ then is $N_1 \in \mathcal{M}_{\mu}$?

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