List questions from measure-theory

Published on 10 Apr 2026 - 15:06

72

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$\phi$ invariant Borel probability measure

Published on 15 Apr 2026 - 7:30

665

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How interpret convergence in probability?

Published on 08 Apr 2026 - 23:14

839

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Cavalieri's Principle

Published on 12 Apr 2026 - 10:54

529

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Sigma algebra unequal to its universal completion

Published on 12 Apr 2026 - 18:21

1k

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Some basic results of measure theory in complex analysis?

Published on 10 Apr 2026 - 14:54

71

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$\lim_n \int_{\frac{1}{n}\leq |f|\leq n} |f|\,d\mu=\int |f| \,d\mu$.

Published on 15 Apr 2026 - 7:05

26

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About a bound on the measure of $B_q := \{x \in X : \exists i_1 < \dots < i_q \text{ with } x \in A_{i_j}\}$ for some $(A_i)_{i\geq 1}$

Published on 15 Apr 2026 - 6:07

43

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If $ \big| \int^b_a f(t,x)- f(s,x)\,\, dx\big|\leq C(b-a)(t-s)$, then $|f(t, x) − f(s, x)| \leq C(t − s)$

Published on 16 Apr 2026 - 18:24

270

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Probability measure induced by a measurable function of a random variable

Published on 10 Apr 2026 - 14:30

826

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Is the Graph of a Measurable Function Measurable?

Published on 16 Apr 2026 - 12:20

67

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How can I prove that $\int X(\omega )\,d\mathbb P(\omega )=\int x\,dF$ ? And what does $\mathbb P(\omega )$ mean?

Published on 15 Apr 2026 - 4:56

126

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Proving a result on Lipschitz functions

Published on 12 Apr 2026 - 0:45

191

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Use Dominated Convergence theorem in Schwartz convergent sequence

Published on 15 Apr 2026 - 6:49

596

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Derive Outer Measure from $\sigma$-Algebra

Published on 10 Apr 2026 - 23:49

List Question

A non-negative function that is bounded by its integral

$\phi$ invariant Borel probability measure

How interpret convergence in probability?

Cavalieri's Principle

Sigma algebra unequal to its universal completion

Some basic results of measure theory in complex analysis?

$\lim_n \int_{\frac{1}{n}\leq |f|\leq n} |f|\,d\mu=\int |f| \,d\mu$.

About a bound on the measure of $B_q := \{x \in X : \exists i_1 < \dots < i_q \text{ with } x \in A_{i_j}\}$ for some $(A_i)_{i\geq 1}$

If $ \big| \int^b_a f(t,x)- f(s,x)\,\, dx\big|\leq C(b-a)(t-s)$, then $|f(t, x) − f(s, x)| \leq C(t − s)$

Probability measure induced by a measurable function of a random variable

Is the Graph of a Measurable Function Measurable?

How can I prove that $\int X(\omega )\,d\mathbb P(\omega )=\int x\,dF$ ? And what does $\mathbb P(\omega )$ mean?

Proving a result on Lipschitz functions

Use Dominated Convergence theorem in Schwartz convergent sequence

Derive Outer Measure from $\sigma$-Algebra

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