Recent content by David1234

Thanks... I will have a look at "Real Analysis and Probability" by Ash.

Thanks a lot for the detail answer. I guess by Chang you mean Kai Lai Chung... :)

I guess if P(w) has a derivative we can write it that way. I got the expression from a textbook by Patrick Billingsley. Generally, when P(w) is not differentiable (as shown in the example), we can not write the expression in that form.

P(dw) is like a distribution fuction... may be. I am confused about P(dw), is it probability of dw? Then what is dw? Following the above example, say, we have f(w)=1 for w=1 and 0 otherwise. What is the meaning of dw here and hence value of P(dw) at w=1? I guess the above integral would give...

What does it mean by \int f(w) P (dw) I don't really understand P (dw) here. Does it mean P (x: x \in B(x, \delta)) for infinitely small \delta ? For example, with P(x)=1/10 for x=1, 2, ..., 10 . How can we interpret this in term of the above integral Thanks...