In mathematics, uniformity is a property of a set or a family of sets that determines how "similar" they are to each other. Specifically, a set or family of sets is said to be uniform if it has some regularity or structure that allows us to make certain predictions or statements about all of its elements. For example, a uniform sequence of sets is one in which each set has the same structure, such as having the same number of elements or the same topology. Similarly, a uniform distribution is one in which each value has an equal probability of occurring. The concept of uniformity is important in many areas of mathematics and science, including probability theory, topology, and analysis.
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