I was just about to ask the same question, specifically for a measure theoretic treatment of probability theory. I've only read/still am reading Measure Theory and Probability Theory by Athreya and Lahiri for the second of a two course sequence and am not too impressed. For one, there are many typos that decrease the readability unless you're already familiar with measure theory and functional analysis (I was not). I haven't read any other texts of this nature, so I can't make any comparisons.