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measurable function of two variables that depends only on the second argument is measurable wrt. its second argument.

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#measure-theory #measurable-functions
208
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Proving that a real-valued function is measurable.

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#limits #lebesgue-integral #measurable-functions #measurable-sets
33
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Doubt on justification for measurability of a function.

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#functions #measurable-functions #measurable-sets
667
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$f:B\to\mathbb{R}$ measurable then $g:\mathbb{R}\to\mathbb{R},g(x)=\begin{cases} f(x) & x\in B\\ 0 & x\in\mathbb{R}\setminus B\end{cases}$ measurable

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#real-analysis #measure-theory #solution-verification #measurable-functions
302
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Principle of measurable choice

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#general-topology #measure-theory #solution-verification #measurable-functions #borel-sets
191
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Integrating with the counting measure

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#integration #measure-theory #lebesgue-measure #measurable-functions #fubini-tonelli-theorems
217
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Measurability of random eigenvectors and random eigenvalues

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#matrices #measure-theory #eigenvalues-eigenvectors #solution-verification #measurable-functions
184
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The Dirichlet function restricted to the irrationals is continuous

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#measure-theory #continuity #measurable-functions
1.3k
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Every continuous function is Borel measurable.

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#measure-theory #measurable-functions
130
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Unitary-transformation invariant measure on subset of the sphere

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#measure-theory #lebesgue-measure #measurable-functions
130
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Random variable function is random variable?

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#probability-theory #measure-theory #random-variables #measurable-functions
66
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Monotonic non borel measurable function

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#real-analysis #measure-theory #measurable-functions #borel-sets
275
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$\{x:f(x)\le g(x)\}$ measurable?

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#measure-theory #measurable-functions #borel-sets
62
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The outer measure of the whole space is $\infty$

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#sequences-and-series #measure-theory #supremum-and-infimum #measurable-functions
35
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Is $X$ measurable from $F$ to Borel sets of $\mathbb{R}$?

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#real-analysis #analysis #lebesgue-measure #measurable-functions

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