Strong convergence refers to a type of convergence in mathematical analysis, particularly in the context of sequences or series. It occurs when a sequence of random variables converges to a limit in such a way that the probability of the difference between the sequence and the limit being greater than a certain value approaches zero as the sequence progresses. This means that the values of the sequence get increasingly close to the limit with high probability. In contrast to weak convergence, which focuses on the convergence of distribution functions, strong convergence emphasizes the actual values of the sequence. It is often used in probability theory and statistics, particularly in relation to concepts like law of large numbers and central limit theorem. Strong convergence ensures that not only do the averages converge, but the individual outcomes do as well.