Introduction to Lebesgue Integration for Statistical Use I am studying statistics at the graduate level and have a moderate background in real analysis however I unfortunately have no experience with Lebesgue integration. 
Does anyone have some recommended textbooks or course web pages or other readings specifically for someone who wants to be able to use/apply Lebesgue integration techniques in a statistical setting? I am not looking for anything too rigorous, for now all I want is a working knowledge of the technique. 
The question in the back of my mind is really an attempt to try to understand how to integrate over the product of PDFs and indicator functions. I have also heard professors allude to some probabilistic shortcuts and more convenient ways of integrating with respect to measurable sets but I don't even know where to begin looking into these techniques. 
Any advice on where to start reading would be helpful. I hope this is not too much of a repeat question. (Other similar questions I have encountered received no useful answers.) If my question is unclear, I will edit later. 
 A: When it comes to the very basics (what's a $\sigma$-algebra, what's a measure, what's a simple function, what's a measurable function, how do we define the integral using simple functions), I would say that a working knowledge and a full understanding are essentially the same. In other words, I think you will need to learn those parts to have any success in using Lebesgue integration. 
In between there and the derivation of the main theorems, there is some work which I don't think you necessarily need to understand. For example, I don't think you need to be able to prove Fatou's Lemma. But then the main theorems themselves are necessary for application. In fact I would say that for a lot of applications, these theorems (the convergence theorems, primarily) are why you would want Lebesgue integration in the first place.
So with your goals, I'd suggest just picking up a graduate real analysis text and getting acquainted with the definitions and the statements of the theorems. Try to do some examples where you check the hypotheses of the theorems. My personal preference for a text like this is Real Analysis by Royden and Fitzpatrick. 
