On regular extensions of measures

Abstract

Let Sf be a sublattice of 2* containing 0,X and let MR{^f) be the collection of all bounded nonnegative finitely additive measures defined on J&(f) the algebra generated by f which are ^-regular in the sense that (E) = Bup(L), LczE, Le f, E eJ/(^), It is shown here that if f x zf are sublattices of 2 X and ju6MB(^i), then extends to a veMR(^2). Several applications are given.