In the 1969 paper "Measure-theoretic uniformity in recursion theory
and set theory," Trans. Amer. Math. Soc. 142 1969 381–420, Sacks gave
a measure-theoretic approach to several results previously obtained by
forcing. For example, he showed that, when countably many random sets
of natural numbers are added to a countable model of ZFC, the result
*with probability 1* is a model of ZF+DC+all sets of reals are measurable.

This seems to me a very enlightening view of Solovay's theorem, yet Sacks' paper is almost unknown. (It has 10 citations on MathSciNet, compared with 98 for Solovay's.) Is there any good reason for the relative neglect of Sacks' paper?

isa kind of forcing, namely, forcing with the measure algebra, as opposed to the Cohen algebra. When one says with random-real forcing that a result holds "with probability one", one is really saying that every forcing extension by that forcing notion has that property. I haven't looked at that paper recently, but I am confused by your description of it, since I had understood that results of Shelah show that one needs an inaccessible cardinal to achieve the consistency of the theory. $\endgroup$ – Joel David Hamkins Feb 8 '13 at 23:41