Preparing for 2nd-year Stat PhD coursework?

[znw]

There's a nice thread in this forum that covers topics worth reviewing before starting up a grad program in statistics, but I wasn't able to find any threads providing recommendations on how to prepare for 2nd-year Stat PhD coursework, which I understand tends to a big jump from 1st-year coursework/Casella & Berger in terms of required mathematical maturity.

Does anyone have recommendations for texts, self-study strategies, or other resources that provided good preparation for their 2nd-year PhD coursework? In my program, the 2nd-year probability/measure theory course has a reputation for being particularly challenging, so recommendations for gaining exposure/an introduction to measure theory would be particularly welcome to this 1st-year student.