= Probabilistic use of Hölder's inequality
On a <probability space>, the same <inequality> reads
$$
\mathbb E|XY|\leq
(\mathbb E|X|^p)^{1/p}(\mathbb E|Y|^q)^{1/q}.
$$
If the displayed <moments> are finite, the product is an <integrable random variable>. The <random variables> can be dependent: the estimate controls their possible overlap without assuming a factorization of the <expected value>. This is useful when a calculation needs the product to be integrable but the joint <probability distribution> is complicated.
Back to article page
