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In this survey the authors endeavor to give a comprehensive examination of the theory of measures having values in Banach spaces. The interplay between topological and geometric properties of Banach spaces and the properties of measures having values in Banach spaces is the unifying theme. The first chapter deals with countably additive vector measures finitely additive vector measures, the Orlicz-Pettis theorem and its relatives. Chapter II concentrates on measurable vector valued functions and the Bochner integral. Chapter III begins the study of the interplay among the Radon-Nikodym theorem for vector measures, operators on $L_1$ and topological properties of Banach spaces.A variety of applications is given in the next chapter. Chapter V deals with martingales of Bochner integrable functions and their relation to dentable subsets of Banach spaces. Chapter VI is devoted to a measure-theoretic study of weakly compact absolutely summing and nuclear operators on spaces of continuous functions. In Chapter VII a detailed study of the geometry of Banach spaces with the Radon-Nikodym property is given. The next chapter deals with the use of Radon-Nikodym theorems in the study of tensor products of Banach spaces. The last chapter concludes the survey with a discussion of the Liapounoff convexity theorem and other geometric properties of the range of a vector measure. Accompanying each chapter is an extensive survey of the literature and open problems

## About book:

## About file:

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- Series:
**Mathematical Surveys and Monographs 015** - Author:
**J. J. Uhl** - Year:
**1977** - Publisher:
**Amer Mathematical Society** - Language:
**English** - ISBN:
**0-8218-1515-6,9780821815151**

- DPI:
**600** - File size:
**5 161 902** - Format:
**djvu**

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This book presents nine survey articles addressing topics surrounding positivity, with an emphasis on functional analysis. The book assembles a wide spectrum of research into positivity, providing up-to-date information on topics of current interest. The ...

Operator theory and functional analysis have a long tradition, initially being guided by problems from mathematical physics and applied mathematics. Much of the work in Banach spaces from the 1930s onwards resulted from investigating how much real (and co...

Accurate fluid level measurement in dynamic environments can be assessed using a Support Vector Machine (SVM) approach. SVM is a supervised learning model that analyzes and recognizes patterns. It is a signal classification technique which has far greater...

Based on the Workshop on Emerging Infections held February 6-7, 2000. Text discusses containment of resistance in microbes, vectors, and animal and human hosts. Covers the methods and measures of a response for industry, federal regulation, public health,...

Since 1968 the Elementary and Secondary School Civil Rights Compliance Report (known as the E&S survey) has been used to gather information about possible disparities in access to learning opportunities and violations of students' civil rights. Thirty-fiv...

Ordinary differential equations play a central role in science and have been extended to evolution equations in Banach spaces. For many applications, however, it is difficult to specify a suitable normed vector space. Shapes without a priori restrictions,...

The U.S. Department of Health and Human Services is carrying out an ambitious new program to assure that funds for public health programs are spent as effectively as possible. Under the new program, every state will develop a set of performance objectives...

Diseases transmitted by insects continue to have a major impact on human populations. Malaria, dengue, onchocerciasis, sleeping sickness and leishmaniasis all adversely affect man. Malaria is one of the most important causes of child mortality and reduces...