Question

Let $S_1,S_2$ be measurable with $d(S_1,S_2)>0$. Show that $\mu(S_1\cup S_2)=\mu S_1+\mu S_2$

score 65 · Answer 1 · 2026-04-17 09:33:25

65

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Let $S_1,S_2$ be measurable with $d(S_1,S_2)>0$. Show that $\mu(S_1\cup S_2)=\mu S_1+\mu S_2$

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score 478 · Answer 2 · 2026-04-11 18:16:13

478

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490

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34

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51

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127

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score 295 · Answer 7 · 2026-05-10 19:14:35

295

Views

Show example $E \subset \mathbb{R}^n$ where exterior measure does not equal that of the smallest open ball cover.

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score 98 · Answer 8 · 2026-04-11 21:26:29

98

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117

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score 36 · Answer 10 · 2026-05-15 22:55:57

36

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135

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score 39 · Answer 12 · 2026-04-17 10:02:48

39

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score 483 · Answer 13 · 2026-04-16 14:36:13

483

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score 133 · Answer 14 · 2026-05-16 20:29:15

133

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score 79 · Answer 15 · 2026-04-08 22:24:43

79

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List Question

Let $S_1,S_2$ be measurable with $d(S_1,S_2)>0$. Show that $\mu(S_1\cup S_2)=\mu S_1+\mu S_2$

Change of variables Expectation

Extending Fubini's Theorem to general joint distributions

Does this definition of the Fourier intensity measure make sense?

Null sets for integration with respect to vector measures

The Diagonal in $R^2$ has measure $0$

Show example $E \subset \mathbb{R}^n$ where exterior measure does not equal that of the smallest open ball cover.

Proof using tonelli's theorem

An inner product?

What does it mean for a map taking a measure to an integral to be continuous?

Verifying some examples of sigma algebra of measurable sets

For bounded functions, Convergence in measure implies convergence in $L^1$

Understanding tightness of a set of measures (any subset of a tight set is tight)

Basic approximation lemma for Lebesgue sets

A translation operator on measures

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