This is problem from Moschovakis' book, problem x10.5., p.153.
In the hint the author refers to the proof of another theorem on p. 153.
The same problem was posted here:
Re: analytic pointset, Baire space (In this thread Henno Brandsma gave a pointer to a proof of this fact in Jech's set theory.)
S.O.S. Mathematics CyberBoard :: View topic - analytic pointset, Baire space
Art of Problem Solving • View topic - analytic pointset, Baire space In this point I tried to explain the hint in the way it is given in the book (since I do not find the context given in the post sufficient.)
(I'm posting these links in order to save the time of the helpers - in case the problem will be solved in one of the forums.)