Question

Linear functionals on the space of measurable functions.

score 618 · Answer 1 · 2016-12-19 11:45:41

618

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Linear functionals on the space of measurable functions.

Published on 19 Dec 2016 - 11:45

score 88 · Answer 2 · 2016-12-20 00:27:44

88

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Is this integral bounded below by a positive number given that a similar integral is?

Published on 20 Dec 2016 - 0:27

score 240 · Answer 3 · 2016-12-20 08:46:46

240

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Proving the existence of a continuous increasing function.

Published on 20 Dec 2016 - 8:46

score 381 · Answer 4 · 2026-04-07 17:57:06

381

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An exercise in the properties of Lebesgue integrals

Published on 07 Apr 2026 - 17:57

score 572 · Answer 5 · 2026-03-27 15:06:30

572

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Trigonometric system is complete proof-Lebesgue Integration by parts

Published on 27 Mar 2026 - 15:06

score 89 · Answer 6 · 2016-12-21 17:49:42

89

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Is this an application of DCT

Published on 21 Dec 2016 - 17:49

score 1.3k · Answer 7 · 2026-04-02 01:46:07

1.3k

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Clarification on the meaning of dx in the integral and differential setting

Published on 02 Apr 2026 - 1:46

score 289 · Answer 8 · 2016-12-24 00:39:42

289

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Continuity of Lebesgue Integral of a Function in 2 Variables

Published on 24 Dec 2016 - 0:39

score 2.1k · Answer 9 · 2016-12-26 23:42:02

2.1k

Views

Lebesgue integration on $[0,1]$ of $x^\alpha$

Published on 26 Dec 2016 - 23:42

score 923 · Answer 10 · 2016-12-27 20:11:31

923

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Limit of Lebesgue Integrals $\lim_{n\to \infty} \int_{[0,\infty]} \frac{n\sin(\frac{x}{n})}{x(1+x^2)}dm$

Published on 27 Dec 2016 - 20:11

score 296 · Answer 11 · 2016-12-28 17:19:37

296

Views

Uniqueness of simple unsigned integral

Published on 28 Dec 2016 - 17:19

score 752 · Answer 12 · 2016-12-28 20:31:58

752

Views

The "dx" in the Lebesgue integral.

Published on 28 Dec 2016 - 20:31

score 136 · Answer 13 · 2016-12-29 23:06:29

136

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Let $f_n \ge 0$ converge pointwise to $f$ and any for simple function $\rho (x)\leq f(x)$ show that $\int\rho d\mu \leq \int f_n d\mu$

Published on 29 Dec 2016 - 23:06

score 665 · Answer 14 · 2016-12-30 07:02:50

665

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$f_n \rightarrow f$ a.e and $\int_\mathbb{R} f_n dm \rightarrow \int_\mathbb{R} f dm$ implies $\int_E f_n dm \rightarrow \int_E f dm$

Published on 30 Dec 2016 - 7:02

score 2.3k · Answer 15 · 2016-12-30 11:18:45

2.3k

Views

Proof verification (to show that every continuous function is measurable)

Published on 30 Dec 2016 - 11:18

List Question

Linear functionals on the space of measurable functions.

Is this integral bounded below by a positive number given that a similar integral is?

Proving the existence of a continuous increasing function.

An exercise in the properties of Lebesgue integrals

Trigonometric system is complete proof-Lebesgue Integration by parts

Is this an application of DCT

Clarification on the meaning of dx in the integral and differential setting

Continuity of Lebesgue Integral of a Function in 2 Variables

Lebesgue integration on $[0,1]$ of $x^\alpha$

Limit of Lebesgue Integrals $\lim_{n\to \infty} \int_{[0,\infty]} \frac{n\sin(\frac{x}{n})}{x(1+x^2)}dm$

Uniqueness of simple unsigned integral

The "dx" in the Lebesgue integral.

Let $f_n \ge 0$ converge pointwise to $f$ and any for simple function $\rho (x)\leq f(x)$ show that $\int\rho d\mu \leq \int f_n d\mu$

$f_n \rightarrow f$ a.e and $\int_\mathbb{R} f_n dm \rightarrow \int_\mathbb{R} f dm$ implies $\int_E f_n dm \rightarrow \int_E f dm$

Proof verification (to show that every continuous function is measurable)

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