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Is this a measurable function is this space?

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#measure-theory #lebesgue-integral #characteristic-functions
2.1k
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Example : Iterated integral and Fubini Theorem

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#real-analysis #integration #lebesgue-integral
242
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Showing a value of certain integral by applying Fubini's Theorem

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#real-analysis #integration #lebesgue-integral
247
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Vitali convergence and convergence in measure

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#lebesgue-integral #lebesgue-measure
90
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Show that $\int f_2(x)dx=\frac{1}{2}\int f(x)dx$ if $f_2(x)=f(2x)$.

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#lebesgue-integral #lebesgue-measure
82
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How to prove this integral inequality

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#real-analysis #integration #lebesgue-integral #lebesgue-measure
344
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A Lebesgue integral problem that seems very intuitive!

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#measure-theory #lebesgue-integral #lebesgue-measure
216
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Linear map from $L^1 \rightarrow L^{\infty}.$

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#real-analysis #analysis #functional-analysis #operator-theory #lebesgue-integral
440
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Integral separation

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#integration #definite-integrals #lebesgue-integral
364
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Application of Differentiation using Lebesgue Dominated Convergence Theorem

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#measure-theory #derivatives #lebesgue-integral #lebesgue-measure
517
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An exercise about Lebesgue integrable functions & convergence

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#real-analysis #integration #measure-theory #lebesgue-integral
113
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Failure of dominated convergence theorem but the result still holds(?).

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#real-analysis #functional-analysis #measure-theory #lebesgue-integral
6.6k
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How much do we really care about Riemann integration compared to Lebesgue integration?

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#real-analysis #integration #lebesgue-integral #riemann-integration
43
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Question about simple functions

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#real-analysis #integration #probability-theory #measure-theory #lebesgue-integral
1.3k
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What is a counterexample to the converse of this corollary related to the Dominated Convergence Theorem?

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#real-analysis #integration #probability-theory #measure-theory #lebesgue-integral

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