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Integral notation?

  1. Jun 29, 2009 #1
    Reading parts of the Monte Carlo methods book by G. Fishman I stumbled into this:

    it says that whenever [tex]\zeta(R) = \int_R \varphi\ dx[/tex] exists, its value is the same as the Lebesgue-Stieltjes integral [tex]\zeta = \int_Z \kappa(z)dF(z)[/tex].

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

    Thanks in advance.
  2. jcsd
  3. Jun 29, 2009 #2


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    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.
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