Vector measures with values in Banach-Kantorovich spaces (Q1589027)

Let \((\Omega, \Sigma, \lambda)\) be a space with a finite measure, \(L_0(\Omega)\) be the ring of equivalence classes of measurable functions on \((\Omega, \Sigma, \lambda)\), \(X\) a measurable Banach bundle with a lifting over \(\Omega\),and \(L_0(\Omega, X)\) the Banach-Kantorovich spaces. The author obtains a decomposition of a Boolean algebra with an \(L_0(\Omega, X)\)-valued measure of finite variation, into a measurable bundle of complete Boolean algebras with \(X(\omega)\)-valued measures.