A Radon-nikodym theorem for positive operators

II A RADON - NIKODYM THEOREM FOR POSITIVE OPERATORS (M. Sc. Thesis) Ayşe UYAR GAZİ UNIVERSITY TNSTITUE OF SCIENCE AND TECHNOLOGY September 1994 ABSTRACT In this thesis work we have studied the following papers by W.A.J. Luxemburg - A.R. Schep: "A Radon-Nikodym type theorem for positive operators and a dual" and by W.A.J. Luxemburg - C.B. Huijmans: "An alternative proof of a Radon-Nikodym theorem for lattice homomorphisms" In the above papers the classical Hahn decomposition theorem and Radon- Nikodym theorem have been generalized for positive operators. In the present work, we have collected the necessary definitions and results about the subject. We have given detailed proofs of their theorems.