Theory of quaternion measures

Abstract

This thesis is a study of a new area of analysis, quaternion measure theory, which is a generalization of positive measure theory, Since the quaternions H are non commutative, we need to define left intergration and right integration. In this thesis we can prove Lebesgue-Radon-Nikodym Theorem, Fubini Theorem, Lebesgue's Monotone Convergence Theorem, Lebesgue's Dominated Convergence Theorem and Riesz Representation Theorem for quaternion measures.