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Measure Theory Fundamentals

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Multiple Choice

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)?

  1. (\mu(\emptyset) = 0)
  2. (\mu(A \cup B) = \mu(A) + \mu(B)) for disjoint sets (A) and (B)
  3. (\mu(A) \leq \mu(B)) whenever (A \subseteq B)
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