Coalitionally strategyproof functions depend only on the most-preferred alternatives

In a framework allowing infinitely many individuals, I prove that coalitionally strategyproof social choice functions satisfy "tops only." That is, they depend only on which alternative each individual prefers the most, not on which alternative she prefers the second most, the third,\dots, or the least. The functions are defined on the domain of profiles measurable with respect to a Boolean algebra of coalitions. The unrestricted domain of profiles is an example of such a domain. I also prove an extension theorem.