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For $f$ periodic, $g\to 0$ the integral of $fg$ converges (under some more conditions)

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#convergence-divergence #lebesgue-integral #periodic-functions
444
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Take the limit of a function inside a Lebesgue integral.

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#analysis #limits #partial-differential-equations #lebesgue-integral
369
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Trace for $L^\infty$ functions?

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#functional-analysis #measure-theory #partial-differential-equations #lebesgue-integral
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Convergence to $\delta$ distribution

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#analysis #distribution-theory #lebesgue-integral #probability-limit-theorems
76
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Relation between integral and distribution

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#real-analysis #measure-theory #lebesgue-integral
117
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Prove that $\int_E cf(x)$ = $c \int_E f(x)$ for measurable E and non-negative f

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#analysis #lebesgue-integral
2.2k
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Why is Lebesgue integral first defined for step function and then for larger classes of functions?

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#real-analysis #integration #definition #lebesgue-integral
2.2k
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Function zero almost everywhere if $\int fg=0$

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#real-analysis #analysis #integration #lebesgue-integral
1.3k
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Total Variation and indefinite integrals

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#real-analysis #measure-theory #lebesgue-integral #bounded-variation
1k
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How to calculate Lebesgue measure?

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#measure-theory #lebesgue-integral
826
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Integration with respect to complex measure

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#measure-theory #lebesgue-integral
43
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Doubt on Lebesgue integration

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#lebesgue-integral
92
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On Lebesgue integration

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#lebesgue-integral
3.8k
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Mean value theorem for Lebesgue integral: $\int_a^bf(t)dt=(b-a)f(c)$ for some $c$.

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#real-analysis #lebesgue-integral
56
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Determine the area of $\phi (A) $

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#real-analysis #analysis #lebesgue-integral

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