Convergence theorems form the backbone of probability theory and statistical inference, ensuring that sequences of random variables behave in a predictable manner as their index grows. These theorems, ...

The paper is concerned with the relationship between various modes of convergence for stochastically monotone sequences of random variables. A necessary and sufficient condition, as well as a ...

This is a preview. Log in through your library . Abstract Convergence in distribution is investigated in a finitely additive setting. Let Xn's be maps, from any set Ω into a metric space S, and P a ...