List questions from lebesgue-integral

Published on 12 Jul 2014 - 0:02

60

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Integrals depending upon a parameter

Published on 12 Jul 2014 - 14:27

145

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Show that $\int_X gdν=\int_X gfdμ$ for all $g∈L_1(ν).$

Published on 15 Jul 2014 - 18:42

88

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$\int_0^1f(x)dx = 2, \int_0^1g(x)dx = 1, \text{and} \int_0^1[f(x)]^2 dx ≤ C$ for some constant $C > 4.$

Published on 16 Jul 2014 - 0:37

87

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$f$ unbounded in $\mathbb{R}$ implies it cannot be in $L^2(\mathbb{R})$.

Published on 16 Jul 2014 - 8:09

59

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Why $\int f_0 \mbox{d}(F_0+F_1)=\int f_0 \mbox{d}F_0+\int f_0 \mbox{d} F_1=1$ should be true?

Published on 16 Jul 2014 - 18:42

1.8k

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Changing the order of integration (for Lebesgue-Stieltjes integral and Riemann integral)

Published on 26 Mar 2026 - 14:21

106

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$L^\infty(\Omega)$ space

Published on 18 Jul 2014 - 9:40

698

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Approximation functions in $L^{1}$ by indicator functions of dyadic cubes

Published on 26 Mar 2026 - 1:09

435

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A Fubini-Tonelli's Theorem Problem

Published on 18 Jul 2014 - 17:45

115

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Absolute continuous function and Jensen inequality

Published on 18 Jul 2014 - 20:01

73

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Let $f_n:\mathbb{R}\rightarrow [0, 1]$ be functions such that $\sup_{x \in \mathbb{R}}f_n(x) = 1/n$ and $||f||_1 = 1$.

Published on 19 Jul 2014 - 19:43

1.2k

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Find a non-negative function on [0,1] such that $t\cdot m(\{x:f(x) \geq t\}) \to 0$ that is not Lebesgue Integrable

Published on 19 Jul 2014 - 21:57

43

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What is the definition of this set of absolutely continuous function

Published on 19 Jul 2014 - 23:09

514

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Spherical coordinates and Lebesgue integral

Published on 20 Jul 2014 - 1:21

List Question

Integration: Countable Additivity?

Integrals depending upon a parameter

Show that $\int_X gdν=\int_X gfdμ$ for all $g∈L_1(ν).$

$\int_0^1f(x)dx = 2, \int_0^1g(x)dx = 1, \text{and} \int_0^1[f(x)]^2 dx ≤ C$ for some constant $C > 4.$

$f$ unbounded in $\mathbb{R}$ implies it cannot be in $L^2(\mathbb{R})$.

Why $\int f_0 \mbox{d}(F_0+F_1)=\int f_0 \mbox{d}F_0+\int f_0 \mbox{d} F_1=1$ should be true?

Changing the order of integration (for Lebesgue-Stieltjes integral and Riemann integral)

$L^\infty(\Omega)$ space

Approximation functions in $L^{1}$ by indicator functions of dyadic cubes

A Fubini-Tonelli's Theorem Problem

Absolute continuous function and Jensen inequality

Let $f_n:\mathbb{R}\rightarrow [0, 1]$ be functions such that $\sup_{x \in \mathbb{R}}f_n(x) = 1/n$ and $||f||_1 = 1$.

Find a non-negative function on [0,1] such that $t\cdot m(\{x:f(x) \geq t\}) \to 0$ that is not Lebesgue Integrable

What is the definition of this set of absolutely continuous function

Spherical coordinates and Lebesgue integral

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