Let C be the class of all probability measure defined on the measurable space ((, A), and
Question:
d(P, Q) = || P - Q || = 2 sup {|P(A) - Q (A)|; A ( A}.
(i) Then show that d is a distance in C; i.e., show that d(P, Q) ( and d(P, Q) = 0 only if P = Q, d(P, Q) = d(Q, P), and d(P, Q) ( d(P, R) + d(R, Q) where R ( C.
Next, let µ be a (-finite measure in A such that P (ii) Then show that
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i The first two properties are immediate and the triangular in...View the full answer
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Related Book For 
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
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