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Verify that if f : (Ω, F ) → (Φ, G ) is a measurable function,...

Verify that if f : (Ω, F ) → (Φ, G ) is a measurable function, and P is a probabil- ity measure on (Ω, F ), then the “pushforward probability measure” defined by Q(B) := P(f−1(B)),∀B ∈ G satisfies the properties of a probability measure.

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