Hello all,

In the chapter 1 of Piterbarg's book in the Radon-Nykodym derivative section, proving the below is referred to as a 'simple conditioning exercise', but I am having great difficulties:

EtQ [Y(T)] = EtP [R Y(T)] / EtP [R]

where :

R = dQ/dP = Radon-Nykodym derivative

P and Q are measures

EtP / EtQ is the conditional expectation wrt given a fitration Ft and measure P/Q

0 <t < T

Y(T) is FT measurable

please can someone suggest some clues ?

In general, to prove the a.s. equality fof 2 random variables X and Y, do I always start from first principles ?

ie prove that for any set A, E (1A X) = E (1A Y) with 1A indicator function of set A

Piterbarg's book is in Prof. Joshi's mandatory reading list which is why I am asking here

Many thanks