The familiar classical results that
(i) any extremally disconnected P-space of nonmeasurable cardinal is discrete, and
(ii) any discrete space of nonmeasurable cardinal is realcompact
are shown to be consequences of much more general results concerning frames. The particular frames involved here are the extremally disconnected 0-dimensional frames in which any countable join of complemented elements is complemented, called almost Boolean, which also have other notable properties. The central result here is that any such frame of nonmeasurable cardinal has discrete spectrum and is realcompact.