Convergence in probability refers to the idea that a sequence of random variables will tend to approach a particular value as the number of trials increases. More formally, a sequence of random variables converges in probability to a random variable if, for every small positive number, the probability that the random variables differ from the value by more than that small number approaches zero as the number of trials goes to infinity. This concept is crucial for understanding the behavior of sequences in probabilistic settings and has significant implications in various fields like martingales and optimization problems.
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