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Almost sure convergence is also called strong convergence of random variables.
The strong convergence of random variables of a probability distribution.
In probability theory, there exist several different notions of convergence of random variables.
This is why the concept of sure convergence of random variables is very rarely used.
Convergence of random variables, for "almost sure convergence"
This article is supplemental for "Convergence of random variables" and provides proofs for selected results.
Convergence of random variables / (LS:R)
The relationships between the various types of continuity of stochastic processes are akin to the relationships between the various types of convergence of random variables.
There are various senses in which a sequence (X) of random variables can converge to a random variable X. These are explained in the article on convergence of random variables.