List questions from lebesgue-measure

Published on 14 Apr 2026 - 1:33

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Function that sends every Lebesgue measureable sets to a lebesgue measurable set. Then it sends measure zero sets to measure zero sets.

Published on 13 Apr 2026 - 23:30

210

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Show that every measurable set $A$ can be written $A=B \cup C$

Published on 15 Apr 2026 - 18:31

314

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Any hint for this measure theory problem from Halmos?

Published on 13 Apr 2026 - 5:59

3.5k

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If $f$ measurable and $B$ a Borel set, then $f^{-1}(B)$ measurable

Published on 16 Apr 2026 - 20:23

241

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lim inf and lim sup question

Published on 14 Apr 2026 - 6:53

88

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If $A_i$ is measurable, prove that $B=\bigcap_{i=1}^\infty \bigcup_{n=i}^\infty A_n$ is a measurable set

Published on 15 Apr 2026 - 21:52

101

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Lebesgue measure of sets

Published on 17 Apr 2026 - 4:14

2.6k

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Measure of non-measurable set is zero

Published on 14 Apr 2026 - 3:20

331

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Is there a null-set whose translations generate the set of all null-sets?

Published on 11 Apr 2026 - 17:51

942

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sup of integrals of simple functions = inf of integrals of simple functions implies f is measurable?

Published on 15 Apr 2026 - 12:26

1.4k

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An example related to the Monotone Convergence Theorem

Published on 15 Apr 2026 - 5:58

227

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Show $\{x:f(x) \neq 0\}$ has measure $0$

Published on 15 Apr 2026 - 9:10

247

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Lebesgue Measurable functions closed under monotone limits

Published on 11 Apr 2026 - 13:02

3k

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Closed Sets are Measurable Proof in Stein/Shakarchi Text

Published on 17 Apr 2026 - 12:51

List Question

Proving that the Lebesgue extension of any measure m is complete

Function that sends every Lebesgue measureable sets to a lebesgue measurable set. Then it sends measure zero sets to measure zero sets.

Show that every measurable set $A$ can be written $A=B \cup C$

Any hint for this measure theory problem from Halmos?

If $f$ measurable and $B$ a Borel set, then $f^{-1}(B)$ measurable

lim inf and lim sup question

If $A_i$ is measurable, prove that $B=\bigcap_{i=1}^\infty \bigcup_{n=i}^\infty A_n$ is a measurable set

Lebesgue measure of sets

Measure of non-measurable set is zero

Is there a null-set whose translations generate the set of all null-sets?

sup of integrals of simple functions = inf of integrals of simple functions implies f is measurable?

An example related to the Monotone Convergence Theorem

Show $\{x:f(x) \neq 0\}$ has measure $0$

Lebesgue Measurable functions closed under monotone limits

Closed Sets are Measurable Proof in Stein/Shakarchi Text

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