In this lecture it will be shown how basic concepts of Probability Theory, such as distribution, independence, (conditional) expectation, can be extended to the case of random sets and random (lower semi-continuous) functions. Then, some convergence results for sequences of random sets and random functions, already known for sequences or real-valued random variables, will be presented. It will be also shown how these results give rise to various applications to the convergence or approximation of some optimization problems. Plan Review on convergence of sequences of sets and functions in the deterministic case. Painleve-Kuratowski's Convergence, epi-convergence, variational properties of epi-convergence. Convex Analysis : conjugate of an extended real-valued function, epi-sum (alias inf-convolution)... Convergence of sequences of sets and functions in a stochastic context Random sets and random functions : denition, notion of equi-distribution and independence, set-valued integral. Strong laws of large numbers, Birkhoś Ergodic Theorem. Conditional expectation and martingales of random sets and random functions, almost sure convergence. Set-valued versions of Fatou's Lemma. Application to the approximation of optimization problems Convergence of discrete epi-sums to continuous epi-sum. Almost sure convergence of estimators. Convergence of integral functionals.