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Measure Theory Fundamentals
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Which of the following is not a property of a measure (\mu) on a set (X): (\mu(\emptyset) = 0), (\mu(A \cup B) = \mu(A) + \mu(B)) for disjoint sets (A) and (B), or (\mu(A) \leq \mu(B)) whenever (A \subseteq B)?
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A
(\mu(A \cup B) = \mu(A) + \mu(B)) for disjoint sets (A) and (B)
💡 Explanation:
The correct answer is (\mu(A \cup B) = \mu(A) + \mu(B)) for disjoint sets (A) and (B). This is known as the additivity property of a measure.