Question

Sequence such that $E_{n} \to E$ and $m(\cup E_{n}) = \infty$ then $\lim_{n} m(E_{n}) > m(\lim_{n} E_{n})$ (Example)

score 42 · Answer 1 · 2018-09-01 00:24:37

42

Views

Sequence such that $E_{n} \to E$ and $m(\cup E_{n}) = \infty$ then $\lim_{n} m(E_{n}) > m(\lim_{n} E_{n})$ (Example)

Published on 01 Sep 2018 - 0:24

score 150 · Answer 2 · 2018-09-01 16:59:19

150

Views

Interchanging a limit and an infinite alternate series

Published on 01 Sep 2018 - 16:59

score 39 · Answer 3 · 2018-09-01 23:24:44

39

Views

Integral of several functions vanishes over a common set

Published on 01 Sep 2018 - 23:24

score 715 · Answer 4 · 2018-09-02 02:07:26

715

Views

Prove if R is a Ring, then R is an algebra iff x $\in$ R (Proof verification)

Published on 02 Sep 2018 - 2:07

score 40 · Answer 5 · 2018-09-03 20:44:23

40

Views

Proving the measure of a set is between 0 and $2\epsilon$ using Countable Sub-additivity

Published on 03 Sep 2018 - 20:44

score 780 · Answer 6 · 2018-09-03 21:52:08

780

Views

Showing that a set is dense in the real numbers.

Published on 03 Sep 2018 - 21:52

score 83 · Answer 7 · 2018-09-05 01:47:01

83

Views

Prove that $m(A) = \int_{0}^{1}f(x)\mathrm{d}x$ where $m$ is Lebesgue Measure.

Published on 05 Sep 2018 - 1:47

score 112 · Answer 8 · 2018-09-05 06:29:43

112

Views

Lebesgue points for vector valued functions

Published on 05 Sep 2018 - 6:29

score 59 · Answer 9 · 2018-09-05 07:48:55

59

Views

Characterisation of compactness in $\mathbb{R}^n$

Published on 05 Sep 2018 - 7:48

score 38 · Answer 10 · 2026-03-27 00:04:16

38

Views

Properties of non-negative integrable functions with 1st, 2nd and 3rd powers having same $L^1$-norm

Published on 27 Mar 2026 - 0:04

score 3k · Answer 11 · 2018-09-05 15:20:44

3k

Views

Show $A$ is a Lebesgue Measurable set $\iff$ there exists $F_\sigma$ set such that $G_\delta$ set $m(G \setminus A) = m(A \setminus F) = 0$

Published on 05 Sep 2018 - 15:20

score 524 · Answer 12 · 2018-09-05 23:01:46

524

Views

Show that $\mu(\bigcap\limits_{n=1}^{\infty}F_{n})=\lim\mu(F_{n})$ can fail if $\mu(F_1) = +\infty$

Published on 05 Sep 2018 - 23:01

score 62 · Answer 13 · 2026-03-25 23:42:22

62

Views

If $T:[0,1] \rightarrow [0,1]$ preserves Lebesgue, then $\liminf_n(n|T^n(x)-x|) \leq 1$

Published on 25 Mar 2026 - 23:42

score 46 · Answer 14 · 2018-09-06 15:22:21

46

Views

Probability theory - computation of interesting form of CDF.

Published on 06 Sep 2018 - 15:22

score 205 · Answer 15 · 2018-09-06 17:56:28

205

Views

Open set in $\mathbb{R}^2$ can be decomposed into pairwise disjoint open balls and a null set

Published on 06 Sep 2018 - 17:56

List Question

Sequence such that $E_{n} \to E$ and $m(\cup E_{n}) = \infty$ then $\lim_{n} m(E_{n}) > m(\lim_{n} E_{n})$ (Example)

Interchanging a limit and an infinite alternate series

Integral of several functions vanishes over a common set

Prove if R is a Ring, then R is an algebra iff x $\in$ R (Proof verification)

Proving the measure of a set is between 0 and $2\epsilon$ using Countable Sub-additivity

Showing that a set is dense in the real numbers.

Prove that $m(A) = \int_{0}^{1}f(x)\mathrm{d}x$ where $m$ is Lebesgue Measure.

Lebesgue points for vector valued functions

Characterisation of compactness in $\mathbb{R}^n$

Properties of non-negative integrable functions with 1st, 2nd and 3rd powers having same $L^1$-norm

Show $A$ is a Lebesgue Measurable set $\iff$ there exists $F_\sigma$ set such that $G_\delta$ set $m(G \setminus A) = m(A \setminus F) = 0$

Show that $\mu(\bigcap\limits_{n=1}^{\infty}F_{n})=\lim\mu(F_{n})$ can fail if $\mu(F_1) = +\infty$

If $T:[0,1] \rightarrow [0,1]$ preserves Lebesgue, then $\liminf_n(n|T^n(x)-x|) \leq 1$

Probability theory - computation of interesting form of CDF.

Open set in $\mathbb{R}^2$ can be decomposed into pairwise disjoint open balls and a null set

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