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Contains an introduction to abstract measure theory and the Lebesgue integral. Standard topics in measure and integration theory are discussed, as are topics on the Hewitt-Yosida decomposition, the Nikodym and Vitali-Hahn-Saks theorems and material on finitely additive set functions.

A presentation of the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. A basic knowledge of introductory real analysis is required of the reader.

The book presents a theory of abstract duality pairs which arises by replacing the scalar field by an Abelian topological group in the theory of dual pair of vector spaces. Examples of abstract duality pairs are vector valued series, spaces of vector valued measures, spaces of vector valued integrable functions, spaces of linear operators and vector valued sequence spaces. These examples give rise to numerous applications such as abstract vers...

- Contains a thorough treatment of each of the integrals of Riemann, Lebesgue, Henstock-Kurzweil and McShane- Discusses the weaknesses of the various integrals and presents a comparison of the integrals- Abundant supply of exercises and examples- Chapters can be used independently

- Contains a thorough treatment of each of the integrals of Riemann, Lebesgue, Henstock-Kurzweil and McShane - Discusses the weaknesses of the various integrals and presents a comparison of the integrals - Abundant supply of exercises and examples - Chapters can be used independently

The notes in this text present a theorem on infinite matrices with values in a topological group due to P. Antosik and J. Mikusinski. Using the matrix theorem and classical gliding hump techniques, applications to various topics in functional analysis, measure theory and sequence spaces are given.

If ? is a space of scalar-valued sequences, then a series ?j xj in a topological vector space X is ?-multiplier convergent if the series ?j=18 tjxj converges in X for every {tj} e?. This monograph studies properties of such series and gives applications to topics in locally convex spaces and vector-valued measures. A number of versions of the Orlicz-Pettis theorem are derived for multiplier convergent series with respect to various locally con...

Digital Cinema" is the process of finishing a motion picture in digital form, distributing the digital file to theaters (on fixed media, by satellite, or over broadband connections), and displaying the motion picture using a digital projector. Professionals trained in traditional motion picture techniques have deep expertise in photochemical technology and need a way to apply that expertise to the new and burgeoning field of digital cinema. Un...

Basic matrix results.- K convergence.- The Uniform Boundedness Principle.- Convergence of operators.- Bilinear maps and hypocontinuity.- Orlicz-Pettis Theorems.- The Schur and Phillips lemma.- The Schur lemma for bounded multiplier convergent series.- Imbedding co and l?.

This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear op...