Question: Let C be the class of all probability measure defined on the measurable space ((, A), and let d(P, Q) = || P - Q

Let C be the class of all probability measure defined on the measurable space ((, A), and let
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

d(P, Q) = | \f g|d .

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