Broadly speaking, I want to read books like [1]. It looks like they use quite a bit of advanced nondiscrete probability. Since I prefer books written in definition - theorem - proof format anyway, I figured I might as well get analysis out the way :)
[1]http://www.cs.cornell.edu/jeh/book%20June%2014,%202017pdf.pd... (Foundations of Data Science by Bloom/Hopcroft/Kannan)