measure (S)

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A function µ defined on a set S which assigns a non-negative value from the extended real numbers to each subset with the properties that µ(φ)=0, µ(AB)=µ(A)+µ(B) if AB=φ. The standard notion of probability is therefore a special case, where the function takes only values in the interval [0, 1]. A function with the above properties but taking negative values also is called a signed measure.

Subjects: Mathematics.

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