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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics specifically, in probability theory the concentration dimension of a Banach space-valued random variable is a numerical measure of how spread out the random variable is compared to the norm on the space. Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. Although an individual coin toss or the roll of a die is a random event, if repeated many times the sequence of random events will exhibit certain statistical patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem.