Vector and Operator Valued Measures and Applications

Vector and Operator Valued Measures and Applications is a collection of papers presented at the Symposium on Vector and Operator Valued Measures and Applications held in Alta, Utah, on August 7-12, 1972. The symposium provided a forum for discussing vector and operator valued measures and their applications to various areas such as stochastic integration, electrical engineering, control theory, and scattering theory.

Comprised of 37 chapters, this volume begins by presenting two remarks related to the result due to Kolmogorov: the first is a theorem holding for nonnegative definite functions from T X T to C (where T is an arbitrary index set), and the second applies to separable Hausdorff spaces T, continuous nonnegative definite functions ? from T X T to C, and separable Hilbert spaces H. The reader is then introduced to the extremal structure of the range of a controlled vector measure ? with values in a Hausdorff locally convex space X over the field of reals; how the theory of vector measures is connected with the theory of compact and weakly compact mappings on certain function spaces; and Daniell and Daniell-Bochner type integrals. Subsequent chapters focus on the disintegration of measures and lifting; products of spectral measures; and mean convergence of martingales of Pettis integrable functions.

This book should be of considerable use to workers in the field of mathematics.

Participants

Preface

Some Remarks on a Theorem of Kolmogorov

On Exposed Points of the Range of a Vector Measure

A Survey of Some Recent Results on Compact Mappings

A Survey of Daniell Integration

Daniell and Daniell-Bochner Type Integrals

Equicontinuity, Absolute Continuity and Weak Compactness in Measure Theory

Independence and Contractive Projections on Lp

Disintegration of Measures and Lifting

The Radon-Nikodym Theorem for Vector Measures with Values in the Duals of Some Nuclear Spaces

Grothendieck Spaces and Vector Measures

Linear Operations on LP-Spaces

A Note on Products of Spectral Measures

Vector Valued Measures and Decomposing Maps

The Yosida-Hewitt Decomposition as an Ergodic Theorem

Stochastic Integration

The Spectral Integral in Scattering Theory

Pre-Measures on Lattices of Sets — II

On the Bochner Integral

The Extension and Closure of Vector Measure

Higher-Order Differentiability of the Norm in Lp(E)

Permanence Properties of Absolute Continuity Conditions

On the Structure of L2,M

Radon-Nikodym Theory for Operator Valued Measures and a Theorem of Foures & Segal

A General Radon-Nikodym Theorem

Stochastic Integration

Stochastic Integral and Vector Valued Measures

Vector-Valued Measures Related to a Generalized Continuous Homogeneous Random Field

Remarks on a Radon-Nikodym Theorem for Vector Measures

Causal Factorization, Shift Operators and the Spectral Multiplicity Function

Integral as a Certain Type of a Positive Definite Function

Vector Measures and the Spectral Theorem

L-Orthogonally Scattered Measures

Absolutely Summing Operators on Cx(S)

S-Bounded Additive Set Functions

Some Remarks on the Notion of "Derivatives"

A Survey of Mean Convergence of Martingales of Pettis Integrable Functions

On the Construction of the Hilbert Space for an Operator-Valued Measure Μ

Bibliography