2021-12-232021-12-2319773908465https://hdl.handle.net/10657/8429In this paper we characterize the continuous linear sufficient statistics for a dominated collection of measures on a Banach space. This is followed by a characterization of exponential families with emphasis on those measures on R[raised n] whose densities with respect to Lebesgue measure are multivariate normal densities. Finally, the relation between Bayes sufficiency and sufficient statistics is studied.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital