Sheaf cohomology theory for measurable spaces (Q1895943)

Let \((\Omega,{\mathfrak A})\) be a measurable space. The author defines a \(\sigma\)-sheaf \({\mathcal F}\) over \((\Omega,{\mathfrak A})\) to be a contravariant functor from the category of \(\sigma\)-subalgebras \({\mathfrak B}\) of \({\mathfrak A}\) and their morphisms to the category of abelian groups. Proceeding in the usual manner he defines the Čech cohomology groups of \((\Omega,{\mathfrak A})\) with coefficients in a \(\sigma\)-sheaf \({\mathcal F}\). He is particularly interested in relating his cohomology groups to the orbit structure of measurable transformation groups.