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f(x+s)=f(x)f(s) imply that f is an exponential function when f(0) = 1.
I was reading a proof for a theorem in Erhan Cinlars intro to stochastic processes textbook that any equation with the following $f(x+s) = f(x)f(s)$, with $f(0)=1$. Then $f(x)=e^{(-ax)}$ for some $a$. ...
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