I am about to complete my master's degree in Statistics at a very well-respected university and one which has a top 5 statistics department in the U.S. (all I have left to do is defend my thesis). I also have a BS Statistics from a top U.S. University as well. Even though I'd like to, I'm doubtful I'll go on to complete a PhD given that (a) I'm older and (b) I work full time.
That being said, I'm very much interested in continuing my studies of statistics in my own time. It seems like one thing I don't have much exposure to formally, but which every PhD statistics student seems to have a good understanding of, is measure theory. Given my background and my desire to learn this material, could the Cross Validated community recommend some introductory measure theory materials and some additional statistics books that you think might be a must-learn or a great way for me to essentially learn some "PhD-level" statistics on my own time? If it's helpful for the recommendations, my interests include survey sampling (especially small area estimation) and imputation, causal inference, longitudinal data analysis and analysis of correlated data.