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How do not generate a $\sigma$-algebra

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#real-analysis #analysis #measure-theory #reference-request #lebesgue-measure
704
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A question relating to uniform integrability and tightness

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#real-analysis #integration #measure-theory #lebesgue-integral #lebesgue-measure
68
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Show that $\lim_{s\rightarrow \infty} e^s m\left( f^{-1}\left([s,\infty)\right) \right) =0$.

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#measure-theory #lebesgue-integral #lebesgue-measure
50
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Suppose $f$ is an integral defined on $[0,b]$, and

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#measure-theory #lebesgue-measure
21
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Approximating the measure of a set using some $[0,c]$

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#real-analysis #lebesgue-measure
7.2k
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Prove that every open set is lebesgue-measurable

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#measure-theory #lebesgue-measure #outer-measure
2k
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Let $\lambda(A)$ be the Lebesgue measure of $A$. There exists an interval $I$ such that $\lambda(E \cap I) / \lambda(I) < 1-\epsilon$

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#measure-theory #lebesgue-measure
347
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Measure of a set invariant under translations with rational numbers

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#real-analysis #measure-theory #lebesgue-measure
87
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An unbounded function with integrability for all p>0

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#real-analysis #lebesgue-integral #lebesgue-measure
161
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Cantor function restriction is onto.

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#lebesgue-measure #cantor-set
160
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Minkowski's theorem generalization

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#measure-theory #algebraic-number-theory #lebesgue-measure
46
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A problem with a Borel set, a continuous function with a fixed point and a non-null fixed set

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#real-analysis #measure-theory #continuity #lebesgue-measure #borel-sets
96
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A problem with a Borel set, a continuous function with a fixed point and a non-null fixed set, II

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#real-analysis #measure-theory #continuity #lebesgue-measure #borel-sets
46
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Does non-zero set contain non-zero sets in each coordinate?

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#measure-theory #lebesgue-measure
307
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Continuity of the expected value of a discontinuous function

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#probability-theory #measure-theory #continuity #lebesgue-measure #expected-value

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