Vol. 86, No. 2, 1980

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On regular extensions of measures

George Bachman and Alan Sultan

Vol. 86 (1980), No. 2, 389–395
Abstract

Let be a sublattice of 2X containing , X and let MR() be the collection of all bounded nonnegative finitely additive measures defined on 𝒜() the algebra generated by which are -regular in the sense that μ(E) = supμ(L), L E,L ∈ℒ,E ∈𝒜(). It is shown here that if 1 ⊂ℒ2 are sublattices of 2X and μ MR(1), then μ extends to a ν MR(2). Several applications are given.

Mathematical Subject Classification 2000
Primary: 28C15
Secondary: 54H99
Milestones
Received: 6 April 1979
Revised: 21 June 1979
Published: 1 February 1980
Authors
George Bachman
Alan Sultan