On the convergence of a bounded amart and a conjecture of Chatterji

Through the decomposition theorem of Lebesgue and Darst it is possible to define a generalized Radon-Nikodym derivative of a bounded additive set function with respect to a bounded countably additive set function. For a bounded amart the derivatives of the components are shown to converge almost everywhere. This result, together with a characterization of amarts, yields a theorem stated by Chatterji whose proof is incorrect.