I'm a math and economics undergraduate interested in econometrics and statistics. I'm trying to put together an independent study course (or courses) that will give me a working understanding of measure and asymptotic theory.
The professor I'm working with (an econometrician) recommended we read thru Asymptotic Statistics (van der Vaart). It looks like a great textbook, but reading the preface the author recommends some understanding of measure theory to get a really good grasp on the proofs. I was curious if anyone had textbook recommendations for a readings course in measure theory that could supplement or precede an asymptotic theory course using van der Vaart.
For an idea of my background, I've taken a probability course that used Larsen and Marx, a first real analysis course that used Cummings ("long-form" textbook, not sure how widely used it is but its easy reading), and a year-long sequence in linear algbera. I have yet to take any courses in abstract algebra or topology, though have seen glimpses of these in other courses. I've taken all of the econometrics courses my school has, mostly applied courses that introduce various estimators and give an intuition for when and how to implement them in research design.
Any recommendations, suggestions, and general pieces of advice are appreciated!
No idea how much prerequisite in measure theory you need. If you are only supposed to be familiar with the basic definitions and ideas, then chapter one and two of Papa Rudin will be helpful. My undergraduate course on Lebesgue integral and measure theory is around that depth. If you need deeper results, then there is a measure theory book by Halmos.