Question

showing that $f: R^n \mapsto R\cup\{\pm\infty\}$ is Lebesgue integrable

score 39 · Answer 1 · 2020-01-16 09:28:02

39

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showing that $f: R^n \mapsto R\cup\{\pm\infty\}$ is Lebesgue integrable

Published on 16 Jan 2020 - 9:28

score 105 · Answer 2 · 2020-01-16 15:19:27

105

Views

Use dominated convergence theorem to show: $\lim_{\ n \to \infty} \| f \ 1_{[n,n+1]} \|_1 = 0$

Published on 16 Jan 2020 - 15:19

score 89 · Answer 3 · 2020-01-17 09:12:17

89

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How do I prove that $\Vert f \Vert_{L^p} := \left(\int^b_a\vert f(x) \vert^p dx \right)^{\frac{1}{p}}$ defines a norm on $C^0([a,b])$?

Published on 17 Jan 2020 - 9:12

score 76 · Answer 4 · 2020-01-17 15:10:53

76

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Numerical Approximation of Lebesgue Integral (Real-Valued)

Published on 17 Jan 2020 - 15:10

score 54 · Answer 5 · 2020-01-17 23:39:00

54

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How I can prove that $T$ is well defined and continuous such that we have :$\|T\|\leq \|g\|_q,$ $T(f)=\int_\Omega f\overline{g}\,d\mu$?

Published on 17 Jan 2020 - 23:39

score 55 · Answer 6 · 2020-01-18 12:23:52

55

Views

Justify the use of Fubini in the case where the product space includes $\Omega$

Published on 18 Jan 2020 - 12:23

score 27 · Answer 7 · 2020-01-18 15:57:01

27

Views

The inclusion of a function in $L^\infty(1, \infty)$, $L^2(1, \infty)$ and $L^3(1, \infty)$

Published on 18 Jan 2020 - 15:57

score 54 · Answer 8 · 2020-01-19 00:10:10

54

Views

A Lebesgue integral into a sum

Published on 19 Jan 2020 - 0:10

score 788 · Answer 9 · 2020-01-19 00:37:07

788

Views

Swapping integral and sum using dominated convergence theorem

Published on 19 Jan 2020 - 0:37

score 56 · Answer 10 · 2020-01-19 13:25:16

56

Views

Defining a continuous function $f \in L^1(0,\infty), L^\infty(0,\infty) : f(t) \not\to 0$ as $t \to \infty$

Published on 19 Jan 2020 - 13:25

score 197 · Answer 11 · 2020-01-21 02:17:12

197

Views

Term by term integration of series on infinite intervals

Published on 21 Jan 2020 - 2:17

score 65 · Answer 12 · 2020-01-21 09:56:23

65

Views

Monotone convergence for Stieltjes integral

Published on 21 Jan 2020 - 9:56

score 177 · Answer 13 · 2020-01-21 23:48:31

177

Views

there exists a measurable set $A$ such that $f = \chi_{A}$ a.e.

Published on 21 Jan 2020 - 23:48

score 133 · Answer 14 · 2020-01-22 13:06:27

133

Views

Is $f(x) = \frac{\cos(x)}{x}$ Lebesgue integrable over $E = [0,1]$?

Published on 22 Jan 2020 - 13:06

score 633 · Answer 15 · 2020-01-22 13:41:57

633

Views

Continuous functions with compact support are dense in $L^1$ (Hypotheses)

Published on 22 Jan 2020 - 13:41

List Question

showing that $f: R^n \mapsto R\cup\{\pm\infty\}$ is Lebesgue integrable

Use dominated convergence theorem to show: $\lim_{\ n \to \infty} \| f \ 1_{[n,n+1]} \|_1 = 0$

How do I prove that $\Vert f \Vert_{L^p} := \left(\int^b_a\vert f(x) \vert^p dx \right)^{\frac{1}{p}}$ defines a norm on $C^0([a,b])$?

Numerical Approximation of Lebesgue Integral (Real-Valued)

How I can prove that $T$ is well defined and continuous such that we have :$\|T\|\leq \|g\|_q,$ $T(f)=\int_\Omega f\overline{g}\,d\mu$?

Justify the use of Fubini in the case where the product space includes $\Omega$

The inclusion of a function in $L^\infty(1, \infty)$, $L^2(1, \infty)$ and $L^3(1, \infty)$

A Lebesgue integral into a sum

Swapping integral and sum using dominated convergence theorem

Defining a continuous function $f \in L^1(0,\infty), L^\infty(0,\infty) : f(t) \not\to 0$ as $t \to \infty$

Term by term integration of series on infinite intervals

Monotone convergence for Stieltjes integral

there exists a measurable set $A$ such that $f = \chi_{A}$ a.e.

Is $f(x) = \frac{\cos(x)}{x}$ Lebesgue integrable over $E = [0,1]$?

Continuous functions with compact support are dense in $L^1$ (Hypotheses)

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