Let be a measurable space and let be two -finite measures defined on . Suppose and is the Radon-Nikodym derivative of with respect to . Define by Show that is a well-defined linear isometry and is an isomorphism if and only if (i.e are mutually absolutely continuous).
Linear Isometry, Radon-Nikodym Derivative and Isomorphisms are investigated. The solution is detailed and well presented.