Lebesgue decomposition by σ-null-additive set functions using ideals

Abstract

Using V. Ficker’s and P. Capek’s algebraic approach by ideals a Lebesgue decomposition theorem for a wide class of non-additive set functions called null-additive set functions is obtained. In special cases decompositions theorems for ⊕-decomposable measures andk-triangular set functions are obtained.