In Oxtoby's book he states thrm 17.1 (Poincaré's recurrence theorem), and deduces it from a generalized form (thrm 17.2). To my understanding, he deduces it in two parts- first he proves that every $x\in G\subset X$ is recurrent, except a nullset, and afterwards he proves the same argument except a set of first category.
These two parts are understandable, but theorem 17.1 states that this is true except a set of first category and measure zero at the same time. I struggle to see why this should be the case after proving each part separately.