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Lebesgue measure of $\mu(A):=\int_A e^{-x} d \lambda(x)$

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#measure-theory #lebesgue-integral #lebesgue-measure
67
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Expected value of a continuous random variable must be strictly bounded

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#probability #measure-theory #lebesgue-integral #lebesgue-measure #expected-value
31
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Does this integral converge over a positive measure?

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#integration #measure-theory #lebesgue-integral #lebesgue-measure
75
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When is a Radon Nikodym derivative integrable?

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#measure-theory #lebesgue-integral
58
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Sum of two indicator functions: $\mathbb{1}_A - \mathbb{1}_B$

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#integration #functional-analysis #analysis #lebesgue-integral
51
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Why do we write f(x) in Lebesgue integrals? (or evaluate anything at x in general inside the integrand)

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#probability-theory #measure-theory #lebesgue-integral
29
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Probability measure vs integral of probability density function

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#measure-theory #lebesgue-integral
155
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A measure space which satisfying $\inf\{\mu(E): E\in M \text{ such that } \mu(E)>0\}=0$

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#real-analysis #measure-theory #lebesgue-integral #lebesgue-measure #lp-spaces
117
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How to calculate the Lebesgue measure of the set $\big\{(x,y)\in [0,1]^2:xy\leq 1/2\big\}$?

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#integration #lebesgue-integral #lebesgue-measure
77
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Differentiability of convolution without compact support

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#real-analysis #lebesgue-integral #lp-spaces #convolution
64
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exchanging limit and integral of a function which tends to infinity in some points

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#calculus #integration #limits #lebesgue-integral #binomial-theorem
49
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Dirac distribution of a product: Simplifying an integral

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#integration #analysis #measure-theory #lebesgue-integral #dirac-delta
89
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why integral converges

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#probability-theory #improper-integrals #lebesgue-integral #sequence-of-function
31
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Proving that $\frac{u}{|x|^{\alpha}}$ is locally integrable for $u \in L^2$

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#real-analysis #integration #lebesgue-integral #distribution-theory #harmonic-analysis
43
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Vanishing of the integral of a strictly positive function

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

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