Question

Examples of Lebesgue-integrable, but not Riemann-integrable functions

score 1.9k · Answer 1 · 2026-03-27 23:40:18

1.9k

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Examples of Lebesgue-integrable, but not Riemann-integrable functions

Published on 27 Mar 2026 - 23:40

score 286 · Answer 2 · 2026-02-23 03:00:03

286

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Is there an invariant measure absolutely continuous wrt to the lebesgue measure for the map f

Published on 23 Feb 2026 - 3:00

score 860 · Answer 3 · 2026-03-25 01:37:04

860

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Let $m^\ast(E)$ < ∞.If for every interval (a, b) we have that $b-a$=$m^\ast((a,b)∩E) + m^\ast((a,b) ∩ E^c)$ then $E$ is lebesgue measurable

Published on 25 Mar 2026 - 1:37

score 54 · Answer 4 · 2019-04-20 17:27:34

54

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If f is differentiable in $[0,1]$, let $E_0=\{x\in [0,1]: f'(x)=0\}$, how to prove $m(f(E_0))=0$($m$ is the Lebesgue measure)?

Published on 20 Apr 2019 - 17:27

score 40 · Answer 5 · 2026-03-29 16:54:25

40

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Find a function satisfies an integrals

Published on 29 Mar 2026 - 16:54

score 68 · Answer 6 · 2019-04-21 19:10:00

68

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Random variable defined on the Lebesgue probability space

Published on 21 Apr 2019 - 19:10

score 170 · Answer 7 · 2026-03-25 17:20:50

170

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Prove that $\lim_{m(I)\rightarrow 0}\frac{m(E\cap I)}{m(I)}=c$ for some $c$ and moving interval $I$.

Published on 25 Mar 2026 - 17:20

score 163 · Answer 8 · 2019-04-23 06:28:30

163

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Showing Lebesgue Integral inequalities

Published on 23 Apr 2019 - 6:28

score 34 · Answer 9 · 2019-04-23 22:11:18

34

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Question about composition of measurable function f and continuous function g being measurable:

Published on 23 Apr 2019 - 22:11

score 69 · Answer 10 · 2019-04-25 15:10:26

69

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Stronger version of finite additivity of Legesgue measure

Published on 25 Apr 2019 - 15:10

score 34 · Answer 11 · 2019-04-26 06:30:20

34

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On density of function spaces

Published on 26 Apr 2019 - 6:30

score 247 · Answer 12 · 2019-04-26 17:36:24

247

Views

Lebesgue integrable implies zero almost everywhere

Published on 26 Apr 2019 - 17:36

score 54 · Answer 13 · 2019-04-26 18:38:09

54

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Existence of a measurable set

Published on 26 Apr 2019 - 18:38

score 345 · Answer 14 · 2026-02-23 06:38:02

345

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Understanding the proof of the deformation lemma

Published on 23 Feb 2026 - 6:38

score 58 · Answer 15 · 2019-04-28 00:57:51

58

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Show that $f_n(x)=x^ne^{-x^2},n≥0$ convergence in $L^p(\lambda,R)$

Published on 28 Apr 2019 - 0:57

List Question

Examples of Lebesgue-integrable, but not Riemann-integrable functions

Is there an invariant measure absolutely continuous wrt to the lebesgue measure for the map f

Let $m^\ast(E)$ < ∞.If for every interval (a, b) we have that $b-a$=$m^\ast((a,b)∩E) + m^\ast((a,b) ∩ E^c)$ then $E$ is lebesgue measurable

If f is differentiable in $[0,1]$, let $E_0=\{x\in [0,1]: f'(x)=0\}$, how to prove $m(f(E_0))=0$($m$ is the Lebesgue measure)?

Find a function satisfies an integrals

Random variable defined on the Lebesgue probability space

Prove that $\lim_{m(I)\rightarrow 0}\frac{m(E\cap I)}{m(I)}=c$ for some $c$ and moving interval $I$.

Showing Lebesgue Integral inequalities

Question about composition of measurable function f and continuous function g being measurable:

Stronger version of finite additivity of Legesgue measure

On density of function spaces

Lebesgue integrable implies zero almost everywhere

Existence of a measurable set

Understanding the proof of the deformation lemma

Show that $f_n(x)=x^ne^{-x^2},n≥0$ convergence in $L^p(\lambda,R)$

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