Question

Equivalence of convergence. In particular $L^p$ and in measure.

score 62 · Answer 1 · 2026-04-11 03:56:24

62

Views

Equivalence of convergence. In particular $L^p$ and in measure.

Published on 11 Apr 2026 - 3:56

score 339 · Answer 2 · 2026-04-16 05:22:59

339

Views

f is measurable function iff $f ^{-1} (A) $ is measurable for every finite set?

Published on 16 Apr 2026 - 5:22

score 970 · Answer 3 · 2026-04-13 23:15:59

970

Views

Prove Outer Measure of $\mathbb R$

Published on 13 Apr 2026 - 23:15

score 56 · Answer 4 · 2026-05-10 14:52:44

56

Views

prove of two sets being equal

Published on 10 May 2026 - 14:52

score 42 · Answer 5 · 2026-04-17 04:41:51

42

Views

Find $m$-measurable sets in $\mathbb R$

Published on 17 Apr 2026 - 4:41

score 106 · Answer 6 · 2026-04-15 04:17:19

106

Views

If $f$ has compact support, choose $x_j \to 0$ so that the functions $f(x - x_j)$ are independent

Published on 15 Apr 2026 - 4:17

score 322 · Answer 7 · 2026-04-11 10:04:16

322

Views

Positive integral on open intervals implies positivity almost everywhere

Published on 11 Apr 2026 - 10:04

score 198 · Answer 8 · 2026-04-11 10:56:14

198

Views

Is this an alternative definition of the Lebesgue integral?

Published on 11 Apr 2026 - 10:56

score 453 · Answer 9 · 2026-04-29 12:23:59

453

Views

Implications of the Borel-Cantelli Lemma

Published on 29 Apr 2026 - 12:23

score 106 · Answer 10 · 2026-04-15 06:10:15

106

Views

Existence of closed $F\subset E$ such that $m(F)=\frac{1}{3}m(E)$ and $m(E)\in(0,\infty),E\subset \mathbb{R}$

Published on 15 Apr 2026 - 6:10

score 246 · Answer 11 · 2026-05-10 14:44:37

246

Views

For a given step function and a given $\epsilon>0$ construct a continuous function which agree outside a set of measure less than $\epsilon$.

Published on 10 May 2026 - 14:44

score 99 · Answer 12 · 2026-04-14 20:33:11

99

Views

Let $\mu$ be the outer measure, then...

Published on 14 Apr 2026 - 20:33

score 841 · Answer 13 · 2026-04-15 01:12:50

841

Views

Any set E of real numbers with positive outer measure contains a subset that fails to be measurable

Published on 15 Apr 2026 - 1:12

score 184 · Answer 14 · 2026-04-14 03:22:18

184

Views

Minkowski sum of two borel sets

Published on 14 Apr 2026 - 3:22

score 35 · Answer 15 · 2026-04-14 06:03:06

35

Views

How to prove that a sequence $f_{n} \in L^{1}$?

Published on 14 Apr 2026 - 6:03

List Question

Equivalence of convergence. In particular $L^p$ and in measure.

f is measurable function iff $f ^{-1} (A) $ is measurable for every finite set?

Prove Outer Measure of $\mathbb R$

prove of two sets being equal

Find $m$-measurable sets in $\mathbb R$

If $f$ has compact support, choose $x_j \to 0$ so that the functions $f(x - x_j)$ are independent

Positive integral on open intervals implies positivity almost everywhere

Is this an alternative definition of the Lebesgue integral?

Implications of the Borel-Cantelli Lemma

Existence of closed $F\subset E$ such that $m(F)=\frac{1}{3}m(E)$ and $m(E)\in(0,\infty),E\subset \mathbb{R}$

For a given step function and a given $\epsilon>0$ construct a continuous function which agree outside a set of measure less than $\epsilon$.

Let $\mu$ be the outer measure, then...

Any set E of real numbers with positive outer measure contains a subset that fails to be measurable

Minkowski sum of two borel sets

How to prove that a sequence $f_{n} \in L^{1}$?

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