Question

$ \lim_{j\rightarrow \infty}\mu(A_j) \implies \lim_{j\rightarrow \infty}\int_{A_j} u d\mu=0, \forall u\in \mathcal L^1(\mu)$

score 56 · Answer 1 · 2019-10-01 09:52:16

56

Views

$ \lim_{j\rightarrow \infty}\mu(A_j) \implies \lim_{j\rightarrow \infty}\int_{A_j} u d\mu=0, \forall u\in \mathcal L^1(\mu)$

Published on 01 Oct 2019 - 9:52

score 195 · Answer 2 · 2014-03-12 16:49:00

195

Views

$f '$ is not Lebesgue integrable on $[-1,1]$

Published on 12 Mar 2014 - 16:49

score 134 · Answer 3 · 2014-03-14 00:09:07

134

Views

Using Riemann integral to define Lebesgue Integral

Published on 14 Mar 2014 - 0:09

score 536 · Answer 4 · 2014-03-16 20:47:10

536

Views

Understanding proof of dominated convergence from Folland.

Published on 16 Mar 2014 - 20:47

score 35 · Answer 5 · 2014-03-17 01:31:32

35

Views

g_n integrable on R

Published on 17 Mar 2014 - 1:31

score 87 · Answer 6 · 2014-03-17 02:19:36

87

Views

There exists an open set such that $vol_n(\Omega)<vol_n(X)+\varepsilon$

Published on 17 Mar 2014 - 2:19

score 72 · Answer 7 · 2026-03-30 23:04:37

72

Views

Boundedness of a sequence of functions

Published on 30 Mar 2026 - 23:04

score 309 · Answer 8 · 2014-03-17 18:22:09

309

Views

Differentiation through the integral sign (Lebesgue integration)

Published on 17 Mar 2014 - 18:22

score 857 · Answer 9 · 2014-03-19 15:50:31

857

Views

Fundamental Theorem of Calculus for Riemann and Lebesgue

Published on 19 Mar 2014 - 15:50

score 60 · Answer 10 · 2026-03-28 01:18:47

60

Views

Identification of $L^2$ limits with distributional convergence

Published on 28 Mar 2026 - 1:18

score 1.4k · Answer 11 · 2014-03-20 15:11:19

1.4k

Views

Continuity of integral of continuous functions

Published on 20 Mar 2014 - 15:11

score 357 · Answer 12 · 2014-03-21 15:27:52

357

Views

Continuity of a parametric integral (where the integrated function is discontinuous)

Published on 21 Mar 2014 - 15:27

score 400 · Answer 13 · 2014-03-21 16:04:27

400

Views

Lebesgue integration: Showing $\lim\limits_{\lambda \rightarrow \infty} \int_{0}^{\infty} e^{-x}\cos(x)\arctan(\lambda x) \ dx = \frac{\pi}{4}$

Published on 21 Mar 2014 - 16:04

score 417 · Answer 14 · 2014-03-22 17:20:19

417

Views

Dominated convergence under weaker hypothesis

Published on 22 Mar 2014 - 17:20

score 369 · Answer 15 · 2014-03-23 15:58:06

369

Views

Jump discontinuity is not a Lebesgue point

Published on 23 Mar 2014 - 15:58

List Question

$ \lim_{j\rightarrow \infty}\mu(A_j) \implies \lim_{j\rightarrow \infty}\int_{A_j} u d\mu=0, \forall u\in \mathcal L^1(\mu)$

$f '$ is not Lebesgue integrable on $[-1,1]$

Using Riemann integral to define Lebesgue Integral

Understanding proof of dominated convergence from Folland.

g_n integrable on R

There exists an open set such that $vol_n(\Omega)<vol_n(X)+\varepsilon$

Boundedness of a sequence of functions

Differentiation through the integral sign (Lebesgue integration)

Fundamental Theorem of Calculus for Riemann and Lebesgue

Identification of $L^2$ limits with distributional convergence

Continuity of integral of continuous functions

Continuity of a parametric integral (where the integrated function is discontinuous)

Lebesgue integration: Showing $\lim\limits_{\lambda \rightarrow \infty} \int_{0}^{\infty} e^{-x}\cos(x)\arctan(\lambda x) \ dx = \frac{\pi}{4}$

Dominated convergence under weaker hypothesis

Jump discontinuity is not a Lebesgue point

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