On regular extensions of measures

George Bachman, Alan Sultan
1980 Pacific Journal of Mathematics  
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 μ(E) = Bupμ(L), LczE, Le £f, E eJ/(^), It is shown here that if £f x τz£f Λ are sublattices of 2 X and ju6MB(^i), then μ extends to a veMR(^2). Several applications are given.
doi:10.2140/pjm.1980.86.389 fatcat:fe5trfrginem3gernkuqadt2h4