I have a little problem which is in part due to my lack in english skills. I am currently reading a book and I dont understand the following chapter (RW stands for random walk): part1
The problem is i dont understand what the author means with $\lambda \in P(\mathbb{R})$ (the set of all probability distributions). What is a probability distribution? THe wikipedia article is not quite clear. Im not sure if $\lambda$ is a distribution function or a probability measure on R. Now up to this point The F and its n-th fold have been distribution functions. But the proof that a standard model always exists would imply that the F's and the $\lambda$ are probability measures now.

thanks in advance

  • $\begingroup$ Its quite clear that Im having a mathematical problem here. And not even wikipedia gives a clear definition, or rather both possibilities as a definition $\endgroup$ – StefanWK Dec 22 '17 at 12:03
  • $\begingroup$ In your link, both $\lambda$ and $F$ are probability measures. $\endgroup$ – fourierwho Dec 23 '17 at 22:36

A probability distribution is a function F(x) defined on the real line with the following properties: $F(x)$ is monotone increasing, $\lim_{x \to -\infty}F(x)=0,\ \lim_{x \to \infty}F(x)=1$.

  • $\begingroup$ No. You are confusing the probability distribution (a measure, thus defined on a sigma-algebra) with its CDF (a function defined on the real line). $\endgroup$ – Did Dec 23 '17 at 22:55

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