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Prove that $\int\sum k\chi_{f^{-1}}<\infty$

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#measure-theory #lebesgue-integral #lebesgue-measure #measurable-functions #measurable-sets
116
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The infinite union of singletons in the Lebesgue measure in $\mathbb{R}$.

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#lebesgue-measure #measurable-sets
31
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Question regarding measurable map and doubt clearing

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#probability #probability-theory #measure-theory #measurable-functions #measurable-sets
112
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Lebesgue measurable function on interval

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#real-analysis #lebesgue-measure #real-numbers #measurable-functions #measurable-sets
752
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The function that generates a measurable graph is measurable

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#measure-theory #measurable-functions #measurable-sets
64
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Numerable union of open measurable sets

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#measurable-sets
121
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Let $f$ be measurable then prove a certain set is measurable.

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#real-analysis #measure-theory #measurable-functions #measurable-sets
211
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Borel-Cantelli Lemma Proof Verification

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#measure-theory #solution-verification #borel-cantelli-lemmas #measurable-sets
797
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Let $E_1 \subset E_2$ both be compact and $m(E_1) = a, m(E_2) = b$. Prove there exists a compact set $E$ st $m(E) = c$ where $a < c < b$.

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#real-analysis #measure-theory #measurable-sets
2.4k
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Proving Caratheodory measurability if and only if the measure of a set summed with the measure of its complement is the measure of the whole space.

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#measure-theory #measurable-sets
170
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Lipshitz function and measurable sets

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#measure-theory #lebesgue-measure #measurable-sets
6.7k
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Proving the *Caratheodory Criterion* for *Lebesgue Measurability*

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#real-analysis #measure-theory #lebesgue-measure #measurable-sets
56
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Problem 2.7.1 in Karatzas and Shreve

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#continuity #stochastic-processes #filtrations #measurable-sets
29
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A notion of equivalence of measurable spaces without bijection between underlying sets?

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#probability-theory #measure-theory #measurable-sets
209
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Let $E ⊆ R$ be a measurable set with |E|> 0. Prove that there exists $a ∈R, a\not= 0$, such that $|(E + a) ∩E|> 0$.

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#real-analysis #measurable-sets

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