In
set theory, the random algebra or random real algebra is the
Boolean algebra of
Borel sets of the unit interval modulo the
ideal of measure zero sets. It is used in random forcing to add random reals to a
model of set theory. The random algebra was studied by
John von Neumann in 1935 (in work later published as
Neumann (1998, p. 253)) who showed that it is not isomorphic to the
Cantor algebra of Borel sets modulo
meager sets. Random forcing was introduced by
Solovay (1970).
Bartoszyński, Tomek (2010), "Invariants of measure and category", Handbook of set theory, vol. 2, Springer, pp. 491–555,
MR2768686
Bukowský, Lev (1977), "Random forcing", Set theory and hierarchy theory, V (Proc. Third Conf., Bierutowice, 1976), Lecture Notes in Math., vol. 619, Berlin: Springer, pp. 101–117,
MR0485358