Linear Isometry, Radon-Nikodym Derivative and Isomorphisms
October 1st, 2022
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).
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