Prerequisite maths for 'Statistical Inference' by Casella and Berger

I want to improve my knoweldge of statistics (part pleasure, part work) and have been recommended 'Statistical Inference' by Casella and Berger as a good foundation text at the undergraduate level (also 'Probability and Random Processes' by Grimmett and Stirzaker).

I graduated in science, not mathematics, and feel it assumes a level of maths I don't have, for example, on sigma algebra the line "...it follows that B is closed under countable intersections." really threw me as I've not encountered the term before. That aside, a lot of the probability I've skimmed through looks familiar so I don't think I'm too far off the start line.

Are there any maths subjects, even at the high school level, that are worth revising/learning before working through this book? My calculus is OK, so I'm guessing something on sets? Any help would be greatly appreciated.

• Grimmett is actually a really good book on probability which covers the necessary background set theory and the like. I might recommend reading up to about Chapter 7 in Grimmet before doing Casella and Berger. The nice thing is it’s a book about probability not about all of the machinery needed to eventually do probability, so it’s more beginner friendly than something that throws sigma algebras at you paragraph one. Commented Jun 5, 2019 at 5:49
• Thanks @eepperly16. Is there another branch of maths that gives a more gentle introduction to sigma algebras? It feels like I'm missing a tool box to understand them. I've got both books so I'll follow your advice. Commented Jun 5, 2019 at 6:03
• The other big area of math which uses $\sigma$-algebras is graduate-level real analysis, and that is certainly not going to be a more gentle introduction than you'll find in Grimmet. To supplement, here is a good general reference for sets and functions and stuff (the section on proofs earlier is also good.) It's where I learned most of this stuff. Commented Jun 5, 2019 at 6:26
• Thank you so much @eepperly16, thats helped me so much! Commented Jun 5, 2019 at 8:50