Boundedness in probability
= Boundedness in probability
= Bounded in probability
{synonym}
A sequence of <random variables> $(X_n)$ is bounded in probability when $\lim_{K\to\infty}\sup_n\mathbb P(|X_n|>K)=0$. A sequence converging in <probability> to a finite <random variable> has this property, and its product with a sequence tending to zero in <probability> also tends to zero in <probability>.