Question

Lebesgue measure theory without Caratheodory's method

score 203 · Answer 1 · 2026-04-11 09:40:37

203

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Lebesgue measure theory without Caratheodory's method

Published on 11 Apr 2026 - 9:40

score 351 · Answer 2 · 2026-04-15 10:47:37

351

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Set in $\mathbb{R}^2$ that contains no (non-null) measurable rectangles

Published on 15 Apr 2026 - 10:47

score 1.1k · Answer 3 · 2026-04-13 02:33:47

1.1k

Views

Is there non Lebesgue measurable set in $I^2$ that its every section has measure $0$?

Published on 13 Apr 2026 - 2:33

score 1.3k · Answer 4 · 2026-04-18 08:17:52

1.3k

Views

Showing $\int_E f=\lim_{n\to\infty}\int_E f_n$ for all measurable $E$

Published on 18 Apr 2026 - 8:17

score 735 · Answer 5 · 2026-04-16 22:18:06

If $f$ is Lebesgue measurable, prove that there is a Borel measurable function $g$ such that $f=g$ except, possibly, on a Borel set of measure zero.

score 96 · Answer 6 · 2026-04-11 06:20:51

96

Views

A problem on outer measure and Lebesgue measure I need some help with

Published on 11 Apr 2026 - 6:20

score 998 · Answer 7 · 2026-04-13 18:43:08

998

Views

Measurable sets vs. unions of intervals.

Published on 13 Apr 2026 - 18:43

score 35 · Answer 8 · 2026-04-15 09:58:43

35

Views

What is the probability that probability of a head in a coin toss is x?

Published on 15 Apr 2026 - 9:58

score 223 · Answer 9 · 2026-04-13 13:20:58

Prove that every nonempty open subset of $\mathbb{R}$ can be expressed as a countable disjoint union of open intervals and another problem.

score 464 · Answer 10 · 2026-04-14 19:56:19

464

Views

Does $\{y\in \mathbb{R}^n:\operatorname{rank}((x,y,Ay))=2\}$ have zero Lebesgue measure?

Published on 14 Apr 2026 - 19:56

score 818 · Answer 11 · 2026-04-12 18:36:39

818

Views

Points of intermediate density for a measurable set

Published on 12 Apr 2026 - 18:36

score 66 · Answer 12 · 2026-04-13 19:15:54

66

Views

Can $[0,1]$ be partitioned with the following property?

Published on 13 Apr 2026 - 19:15

score 71 · Answer 13 · 2026-04-12 02:07:45

71

Views

Show that Lebesgue measure is Caratheodory

Published on 12 Apr 2026 - 2:07

score 79 · Answer 14 · 2026-04-15 11:53:56

79

Views

Proving union of two $\sigma$ algebras in $X$ is an algebra, then it is a $\sigma$-algebra.

Published on 15 Apr 2026 - 11:53

score 49 · Answer 15 · 2026-04-18 13:35:55

49

Views

Is this subspace of $L^1(\mathbb{R},m)$ closed?

Published on 18 Apr 2026 - 13:35

List Question

Lebesgue measure theory without Caratheodory's method

Set in $\mathbb{R}^2$ that contains no (non-null) measurable rectangles

Is there non Lebesgue measurable set in $I^2$ that its every section has measure $0$?

Showing $\int_E f=\lim_{n\to\infty}\int_E f_n$ for all measurable $E$

If $f$ is Lebesgue measurable, prove that there is a Borel measurable function $g$ such that $f=g$ except, possibly, on a Borel set of measure zero.

A problem on outer measure and Lebesgue measure I need some help with

Measurable sets vs. unions of intervals.

What is the probability that probability of a head in a coin toss is x?

Prove that every nonempty open subset of $\mathbb{R}$ can be expressed as a countable disjoint union of open intervals and another problem.

Does $\{y\in \mathbb{R}^n:\operatorname{rank}((x,y,Ay))=2\}$ have zero Lebesgue measure?

Points of intermediate density for a measurable set

Can $[0,1]$ be partitioned with the following property?

Show that Lebesgue measure is Caratheodory

Proving union of two $\sigma$ algebras in $X$ is an algebra, then it is a $\sigma$-algebra.

Is this subspace of $L^1(\mathbb{R},m)$ closed?

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