Question

Let $f$ be a bounded measurable function on $E$. Show that there are sequences of simple functions converging uniformly on $E$.

score 5.3k · Answer 1 · 2026-04-14 18:21:36

5.3k

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Let $f$ be a bounded measurable function on $E$. Show that there are sequences of simple functions converging uniformly on $E$.

Published on 14 Apr 2026 - 18:21

score 7.1k · Answer 2 · 2026-04-16 12:20:36

7.1k

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Is the inverse image of $\emptyset$ measurable?

Published on 16 Apr 2026 - 12:20

score 1.6k · Answer 3 · 2026-04-16 23:15:55

1.6k

Views

Proof that the Fat Cantor set is not a null set

Published on 16 Apr 2026 - 23:15

score 3.1k · Answer 4 · 2026-04-16 15:08:25

3.1k

Views

Uniform convergence of simple functions to a bounded function $f$

Published on 16 Apr 2026 - 15:08

score 68 · Answer 5 · 2026-04-13 15:49:04

68

Views

Examining measurability of a function

Published on 13 Apr 2026 - 15:49

score 125 · Answer 6 · 2026-04-12 13:28:39

125

Views

Relating a complex integral to an integral of the real part of a function

Published on 12 Apr 2026 - 13:28

score 61 · Answer 7 · 2026-04-13 04:13:59

61

Views

using the dominated convergence theorem

Published on 13 Apr 2026 - 4:13

score 4.9k · Answer 8 · 2026-04-04 14:47:24

4.9k

Views

A Lipschitz transform maps measurable set to measurable

Published on 04 Apr 2026 - 14:47

score 115 · Answer 9 · 2026-04-25 02:34:21

115

Views

Show that the measure $h(E)= \int_{E} \frac{1}{x} dx$ on Borel sets is invariant under dilations

Published on 25 Apr 2026 - 2:34

score 70 · Answer 10 · 2026-04-25 02:34:07

70

Views

Does a function being Lebesgue measurable imply it is integrable? ($f\colon [a,b]\to\Bbb C$)

Published on 25 Apr 2026 - 2:34

score 695 · Answer 11 · 2026-04-25 04:09:35

695

Views

Fubini–Tonelli theorem

Published on 25 Apr 2026 - 4:09

score 305 · Answer 12 · 2026-04-13 11:16:25

305

Views

Measure of the intersection of open sets

Published on 13 Apr 2026 - 11:16

score 65 · Answer 13 · 2026-04-25 04:18:10

65

Views

Evaluating the limit of $\int_{\mathbb{R}} \frac{1}{x^2+n^2} \cos(\sqrt{x^2+n^2})~d\lambda$ in the lebesgue measure.

Published on 25 Apr 2026 - 4:18

score 662 · Answer 14 · 2026-04-13 07:21:46

662

Views

Finding a dominating function

Published on 13 Apr 2026 - 7:21

score 221 · Answer 15 · 2026-04-13 20:24:40

221

Views

Construction of Outer Measures

Published on 13 Apr 2026 - 20:24

List Question

Let $f$ be a bounded measurable function on $E$. Show that there are sequences of simple functions converging uniformly on $E$.

Is the inverse image of $\emptyset$ measurable?

Proof that the Fat Cantor set is not a null set

Uniform convergence of simple functions to a bounded function $f$

Examining measurability of a function

Relating a complex integral to an integral of the real part of a function

using the dominated convergence theorem

A Lipschitz transform maps measurable set to measurable

Show that the measure $h(E)= \int_{E} \frac{1}{x} dx$ on Borel sets is invariant under dilations

Does a function being Lebesgue measurable imply it is integrable? ($f\colon [a,b]\to\Bbb C$)

Fubini–Tonelli theorem

Measure of the intersection of open sets

Evaluating the limit of $\int_{\mathbb{R}} \frac{1}{x^2+n^2} \cos(\sqrt{x^2+n^2})~d\lambda$ in the lebesgue measure.

Finding a dominating function

Construction of Outer Measures

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