Lebesgue decomposition of contents via nonnegative forms

Abstract

We present a new approach for the Lebesgue decomposition of finitely additive measures (or contents, for short). Using the recently proved results of Hassi, Sebestyen and de Snoo, we show that the Lebesgue decomposition of contents exists, and corresponds to the Lebesgue decomposition of their induced forms. Additionally, we also present some new results related to the almost dominated part of a form (resp., a content).