Question

Lebesgue integral on every interval equal implies two functions must be equal?

score 409 · Answer 1 · 2019-12-02 08:15:26

409

Views

Lebesgue integral on every interval equal implies two functions must be equal?

Published on 02 Dec 2019 - 8:15

score 192 · Answer 2 · 2019-12-02 14:13:17

192

Views

Lebesgue-integrability on a compact set

Published on 02 Dec 2019 - 14:13

score 97 · Answer 3 · 2019-12-02 21:44:05

97

Views

Measure theory question integrable function

Published on 02 Dec 2019 - 21:44

score 453 · Answer 4 · 2019-12-02 23:51:52

453

Views

Is $f(x,y) = \frac{x^{2}-y^{2}}{(x^{2}+y^{2})^{2}}$ Lebesgue integrable?

Published on 02 Dec 2019 - 23:51

score 77 · Answer 5 · 2019-12-04 02:07:25

77

Views

A Lebesgue integration problem

Published on 04 Dec 2019 - 2:07

score 55 · Answer 6 · 2019-12-04 04:48:45

55

Views

Prove that $v_n=\int_{1}^{n}{(1-\frac{x}{n})^{n}} \times \frac{1}{x} \, dx$

Published on 04 Dec 2019 - 4:48

score 64 · Answer 7 · 2019-12-04 15:30:03

64

Views

Calculate $I = \int_{0}^{+\infty}{e^{-{\frac{x^{2}}{2}}}}dx$ using $\int fd\lambda _2$

Published on 04 Dec 2019 - 15:30

score 549 · Answer 8 · 2019-12-04 16:55:36

549

Views

Sequence of functions on $[0,1]$ that converges pointwise to $0$ for all $x$, whose integral converges to $0$, but whose supremum isn't in $L^1$

Published on 04 Dec 2019 - 16:55

score 50 · Answer 9 · 2026-02-23 11:45:23

50

Views

Absolutely continuity and Lipschitz-like continuity

Published on 23 Feb 2026 - 11:45

score 409 · Answer 10 · 2019-12-04 22:58:44

409

Views

Simple functions in $L^{1}(X)$ are dense in $L^{1}(X)$.

Published on 04 Dec 2019 - 22:58

score 59 · Answer 11 · 2026-03-26 07:59:15

59

Views

Show infinite series is the limit of a Cauchy sequence in $L^1(\mathbb{R})$

Published on 26 Mar 2026 - 7:59

score 97 · Answer 12 · 2019-12-06 20:56:54

97

Views

$f \in L^{1}(X)$ and $g:X \to \mathbb{R}$ measurable, such $f=g$ a.e. Prove that $g \in L^{1}(X)$ and $\int_{X} f d \mu = \int_{X} g d \mu $.

Published on 06 Dec 2019 - 20:56

score 246 · Answer 13 · 2026-03-25 06:30:48

246

Views

Bounded Variation Function and its Total Variation

Published on 25 Mar 2026 - 6:30

score 110 · Answer 14 · 2019-12-07 03:18:45

110

Views

Looking for an inequality relating $\int_Efg$ to the integrals $\int_Ef$ and $\int_Eg$

Published on 07 Dec 2019 - 3:18

score 61 · Answer 15 · 2019-12-07 06:29:34

61

Views

Must $f$ necessarily be integrable?

Published on 07 Dec 2019 - 6:29

List Question

Lebesgue integral on every interval equal implies two functions must be equal?

Lebesgue-integrability on a compact set

Measure theory question integrable function

Is $f(x,y) = \frac{x^{2}-y^{2}}{(x^{2}+y^{2})^{2}}$ Lebesgue integrable?

A Lebesgue integration problem

Prove that $v_n=\int_{1}^{n}{(1-\frac{x}{n})^{n}} \times \frac{1}{x} \, dx$

Calculate $I = \int_{0}^{+\infty}{e^{-{\frac{x^{2}}{2}}}}dx$ using $\int fd\lambda _2$

Sequence of functions on $[0,1]$ that converges pointwise to $0$ for all $x$, whose integral converges to $0$, but whose supremum isn't in $L^1$

Absolutely continuity and Lipschitz-like continuity

Simple functions in $L^{1}(X)$ are dense in $L^{1}(X)$.

Show infinite series is the limit of a Cauchy sequence in $L^1(\mathbb{R})$

$f \in L^{1}(X)$ and $g:X \to \mathbb{R}$ measurable, such $f=g$ a.e. Prove that $g \in L^{1}(X)$ and $\int_{X} f d \mu = \int_{X} g d \mu $.

Bounded Variation Function and its Total Variation

Looking for an inequality relating $\int_Efg$ to the integrals $\int_Ef$ and $\int_Eg$

Must $f$ necessarily be integrable?

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