Integral notation?

**oswald2323** · Jun29-09, 07:25 PM

Reading parts of the Monte Carlo methods book by G. Fishman I stumbled into this:

it says that whenever $LaTeX Code: \\zeta(R) = \\int_R \\varphi\\ dx$ exists, its value is the same as the Lebesgue-Stieltjes integral $LaTeX Code: \\zeta = \\int_Z \\kappa(z)dF(z)$ .

I am confused as to what this means, especially the "dF(z)" part.

Thanks in advance.

**mathman** · Jun29-09, 07:45 PM

You need to get a tutorial on Stieltjes integral. Try Google - the Wikipeida articles (Riemann-S and Lebesgue-S, the latter is what is used in the question you raised) should give you a good idea. As far as the Monte Carlo method is concerned, the statement you quoted is a basic theorem of probability theory.