Question

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

score 59 · Answer 1 · 2018-02-25 21:07:56

59

Views

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

Published on 25 Feb 2018 - 21:07

score 336 · Answer 2 · 2018-02-26 15:04:00

336

Views

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

Published on 26 Feb 2018 - 15:04

score 967 · Answer 3 · 2018-02-28 05:20:28

967

Views

Prove Outer Measure of $\mathbb R$

Published on 28 Feb 2018 - 5:20

score 44 · Answer 4 · 2026-03-17 02:34:52

44

Views

prove of two sets being equal

Published on 17 Mar 2026 - 2:34

score 39 · Answer 5 · 2018-02-28 09:20:05

39

Views

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

Published on 28 Feb 2018 - 9:20

score 103 · Answer 6 · 2018-02-28 20:53:39

103

Views

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

Published on 28 Feb 2018 - 20:53

score 319 · Answer 7 · 2018-03-01 01:48:12

319

Views

Positive integral on open intervals implies positivity almost everywhere

Published on 01 Mar 2018 - 1:48

score 195 · Answer 8 · 2018-03-02 19:53:24

195

Views

Is this an alternative definition of the Lebesgue integral?

Published on 02 Mar 2018 - 19:53

score 445 · Answer 9 · 2026-03-20 02:32:33

445

Views

Implications of the Borel-Cantelli Lemma

Published on 20 Mar 2026 - 2:32

score 104 · Answer 10 · 2018-03-03 16:28:25

104

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 03 Mar 2018 - 16:28

score 241 · Answer 11 · 2026-03-17 10:33:46

241

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 17 Mar 2026 - 10:33

score 96 · Answer 12 · 2018-03-04 22:23:41

96

Views

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

Published on 04 Mar 2018 - 22:23

score 838 · Answer 13 · 2018-03-05 01:27:07

838

Views

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

Published on 05 Mar 2018 - 1:27

score 181 · Answer 14 · 2018-03-05 11:17:01

181

Views

Minkowski sum of two borel sets

Published on 05 Mar 2018 - 11:17

score 31 · Answer 15 · 2026-03-22 13:55:02

31

Views

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

Published on 22 Mar 2026 - 13:55

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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