Talk:Moment-generating function/Comments

Is it true that "Regardless of whether the probability distribution is continuous or not, the moment-generating function is given by the Riemann-Stieltjes integral"

When you calculate the MGF of Poisson distribution. X~Poisson(lambda) M_X(t)=E[exp(tX)]=sum(exp(tx)*p(x),x=0,infinity) is the correct formula to use. This is clearly not an integral. Does Riemann-Stieltjes integral include summation as well?