Measure Theory and Functional Analysis (ePub)

This book provides an introduction to measure theory and functional analysis suitable for a beginning graduate course, and is based on notes the author had developed over several years of teaching such a course. It is unique in placing special emphasis on the separable setting, which allows for a simultaneously more detailed and more elementary exposition, and for its rapid progression into advanced topics in the spectral theory of families of self-adjoint operators. The author's notion of measurable Hilbert bundles is used to give the spectral theorem a particularly elegant formulation not to be found in other textbooks on the subject.Request Inspection CopyContents:Topological SpacesMeasure and IntegrationBanach SpacesDual Banach SpacesSpectral TheoryReadership: Graduates students in mathematics (pure and applied) in their first or second year, graduate students in physics or engineering, and economics.Key Features:A very readable and thorough treatment of the core material in measure theory and functional analysis which cuts a clear path to advanced results in the spectral theory of families of commuting self-adjoint operators, avoiding side topics of lesser importancePresents the author's elegant formulation of the spectral theorem in terms of his notion of Hilbert bundles, not available in comparable textbooksUniquely firm emphasis on the separable case allows for a simultaneously more detailed and more elementary expositionIncludes over 150 exercises