New answers tagged almost-everywhere
3
votes
Accepted
$X \in \{-b,0,b\}$ $P$-almost surely if and only if $P(|X| \geq b)=b^{-p}\mathbb{E}|X|^p $
First note that
$$\int_{|X|\geq b}b^pdP\le\int_{|X|\geq b}|X|^pdP
\le\mathbb{E}(|X|^p).$$
If $P(|X| \geq b)=b^{-p}\mathbb{E}(|X|^p)$ then these two inequalities become equalities. The first one ...
- 44.2k
0
votes
Accepted
Prove $f = 0$ Almost Everywhere in $L^1$ Under Given Conditions
One idea thats a bit more explicit is to write $A=\bigcup_{n}\{x: f(x)\geq \frac{1}{n}\}$.
Denote
$A_{n}=\{x: f(x)\geq \frac{1}{n}\}$, you can cover $A_{n}$ by a countable collection of intervals of ...
- 112
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