Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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:

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

share|improve this question
up vote 6 down vote accepted

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

share|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.