Special theorems on Boolean Lattices

Abstract

In chapter [A.] we have discussed basic properties of tribes. They will be applied in this book. The present chapter [A I.] gives some important auxiliary theorems, especially theorems on extension of tribes and measure. There. will be several items: The Wecken’s theorem on complete additivity of tribes, Fréchet’s condition for denumerable additivity of measure, Borelian extension of tribes, an extension theorem on tribes whose somata are sets, classical measure extension devices, a measure extension device by the author and comparison of measure extension device by Lebesgue, by Caratheodory and by the author, measure topology and somatic topology on a tribe.