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Aug 1, 2010 at 3:30 comment added Mark Meckes Actually, it's a Laplace transform. The difference is important: it's possible to find $X_1$ such that $\phi(t)$ diverges except for $t=0$. But the Fourier transform $E(e^{itX})$ is defined for every real-valued random variable and every real $t$.
Aug 1, 2010 at 0:15 history answered Yuval Filmus CC BY-SA 2.5