Earlier quoted context omitted.
Halmos Measure Theory is a good prerequisite to Neveu. Rudin, Principles is a bit too little. Instead, the first half, the real half of Rudin's Real and Complex Analysis is a good prerequisite. So, is Royden's Real Analysis . Neveu is elegant beyond belief, but Breiman, Probability , the SIAM book, available in paperback, is darned good, usually easier than Neveu, less elegant, closer to applications, and without som…
Thanks for the insights. Chung seems quite doable at my current level. I skimmed through it sometime ago. I borrowed a copy of Neveu and it seemed a bit harder. Care to share other references you like. Real & complex analysis and algebra, in particular, are most welcome.
I've mentioned books I've spent at least some significant time with.
There are lots more books on my shelves that look good, have good recommendations, etc. but I haven't paid much attention to.
My interest in algebra is a bit meager -- I'm not seriously interested in number theory, algebraic geometry, algebraic topology, etc.
For real analysis, the books I mentioned seem to me to provide really good sources. Of course there is much more to analysis, e.g., functional analysis. And there's a lot to stochastic processes. And much more to math.