Mathematical knowledge needed for learning upper level statistics im a math student who wants to study statistics in depth for a master degree(maybe doctor degree). And I was wondering what kind of math knowledge might be needed for upper level statistics. I wanna learn statistics in a mathematically rigorous way and understand all the maths behind statistics knowledge.
I have searched relevant questions on a couple platforms and the answers are linear algebra, calculus, and analysis. But what analysis exactly do I need to study? I can think of real analysis, functional analysis, measure theory and maybe a bit of topology?(not very sure if these are actually needed) Are these enough? Is there anything else I need to study in depth or is there anything I don't need to spend too much time on?
Also any math books recommended for learning statistics in a theoretical and mathematical way? I have a couple books in hand such as mathematical methods of statistics by Cramer, but its simply not for me yet. I found it a bit challenging to read(since im still doing my undergrad degree in math) and that's why im asking for some math books to read first and then get back to this book for further study.
Thanks in advance.

As a start to study Statistics mathematically and rigorously, I would recommend you to read:

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*Shao J - Mathematical Statistics
It is a very good book to begin your journey.
