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For a stochastic process with trajectories in $C[0,1]$ why is it that convergence of the finite dimensional distributions is not sufficient for weak convergence,unless we also have relative compactness, however it is sufficient for a sequence of random variables. Every book simply quotes Billingsley but none explains why this is the case, and I can't figure it out,

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What part of Billingsley's discussion is not clear? –  Nate Eldredge May 8 '12 at 3:04
billingsleys is too advanced for me right now, my goal is to start off with easier books and work into that one later in the year, he basically gives two examples to show that in C[0,1] convergence of finite dimensional distributions is not sufficient –  Peter Asden May 8 '12 at 4:24

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