# dG(y) in expected value integral

I am wondering what exactly the notation dG(y) inside an integral means, what it's called and where I can read more about it:

$$E[B_1]=\int_0^{\infty}E[B_1 \vert Y_1 = y] dG(y)$$

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It's the Stieltjes integral, and basically allows for the possibility that $G(x)$ may not have a continuous derivative -- for example, if $G$ is a discrete distribution.

If $G$ does have a continuous derivative, then your expression is the same as the usual Riemann integral

$$\int_0^{\infty}E[B_1 \vert Y_1 = y] g(y) dy$$

where $g(y) = dG(y)/dy$.

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I haven't formally studied it, but I remember looking it up. You really have to turn to a human to look up something based on appearance. I don't think there is a search engine for math notation :) – m33lky May 19 '14 at 3:03