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Vector and Operator Valued Measures and Applications: proceedings of a Symposium; Alta - Ut., August, 7-12, 1972

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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.

Author(s): Tucker, Don H.
Publisher: Academic Press
Year: 1973

Language: English
Pages: 458 S.
City: New York

, Inside Front Cover, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Page ii, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50001-4.

, Front Matter, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Page iii, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50002-6.

, Copyright, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Page iv, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50003-8.

, PARTICIPANTS, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages ix-xiii, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50004-X.

, PREFACE, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages xv-xvi, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50005-1.

G.D. Allen and S. Cambanis, SOME REMARKS ON A THEOREM OF KOLMOGOROV, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 1-5, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50006-3.

R. Anantharaman, ON EXPOSED POINTS OF THE RANGE OF A VECTOR MEASURE, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 7-22, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50007-5.

Jürgen Batt, A SURVEY OF SOME RECENT RESULTS ON COMPACT MAPPINGS, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 23-32, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50008-7.

Klaus Bichteler, A SURVEY OF DANIELL INTEGRATION, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 33-42, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50009-9.

Witold M. Bogdanowicz, DANIELL AND DANIELL-BOCHNER TYPE INTEGRALS, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 43-50, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50010-5.

James K. Brooks, EQUICONTINUITY, ABSOLUTE CONTINUITY AND WEAK COMPACTNESS IN MEASURE THEORY, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 51-61, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50011-7.

Charles Byrne Jr. and Francis Sullivan, INDEPENDENCE AND CONTRACTIVE PROJECTIONS ON Lp, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 63-67, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50012-9.

S.D. Chatterji, DISINTEGRATION OF MEASURES AND LIFTING, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 69-83, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50013-0.

G.Y.H. Chi, THE RADON-NIKODYM THEOREM FOR VECTOR MEASURES WITH VALUES IN THE DUALS OF SOME NUCLEAR SPACES, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 85-95, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50014-2.

J. Diestel, GROTHENDIECK SPACES AND VECTOR MEASURES, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 97-108, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50015-4.

Nicolae Dinculeanu, LINEAR OPERATIONS ON Lp-SPACES, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 109-124, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50016-6.

R.M. Dudley, A NOTE ON PRODUCTS OF SPECTRAL MEASURES, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 125-126, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50017-8.

D.J. Hebert Jr., VECTOR VALUED MEASURES AND DECOMPOSING MAPS, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 127-132, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50018-X.

Robert E. Huff, THE YOSIDA-HEWITT DECOMPOSITION AS AN ERGODIC THEOREM, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 133-139, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50019-1.

Kiyosi Itô, STOCHASTIC INTEGRATION, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 141-148, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50020-8.

J.M. Jauch, W. Amrein and V. Georgescu, THE SPECTRAL INTEGRAL IN SCATTERING THEORY, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 149-153, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50021-X.

J.L. Kelley, M.K. Nayak and T.P. Srinivasan, PRE-MEASURES ON LATTICES OF SETS - II, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 155-164, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50022-1.

J.L. Kelley and T.P. Srinivasan, ON THE BOCHNER INTEGRAL, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 165-174, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50023-3.

Igor Kluvánek, THE EXTENSION AND CLOSURE OF VECTOR MEASURE, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 175-190, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50024-5.

I. Edward Leonard, HIGHER-ORDER DIFFERENTIABILITY OF THE NORM IN LP (E), In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 191-195, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50025-7.

Paul W. Lewis, PERMANENCE PROPERTIES OF ABSOLUTE CONTINUITY CONDITIONS, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 197-206, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50026-9.

V. Mandrekar and H. Salehi, ON THE STRUCTURE OF L 2,M, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 207-215, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50027-0.

P. Masani, RADON-NIKODYM THEORY FOR OPERATOR VALUED MEASURES AND A THEOREM OF FOURES & SEGAL, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 217-232, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50028-2.

Hugh B. Maynard, A GENERAL RADON-NIKODYM THEOREM, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 233-246, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50029-4.

E.J. McShane, STOCHASTIC INTEGRATION, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 247-281, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50030-0.

Michel Metivier, STOCHASTIC INTEGRAL AND VECTOR VALUED MEASURES, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 283-296, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50031-2.

Zoran R. Pop-Stojanovic, VECTOR-VALUED MEASURES RELATED TO A GENERALIZED CONTINUOUS HOMOGENEOUS RANDOM FIELD, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 297-301, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50032-4.

M.M. Rao, REMARKS ON A RADON-NIKODYM THEOREM FOR VECTOR MEASURES*, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 303-317, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50033-6.

R. Saeks, CAUSAL FACTORIZATION, SHIFT OPERATORS AND THE SPECTRAL MULTIPLICITY FUNCTION, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 319-335, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50034-8.

Parfeny P. Saworotnow, INTEGRAL AS A CERTAIN TYPE OF A POSITIVE DEFINITE FUNCTION, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 337-338, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50035-X.

Alan H. Shuchat, VECTOR MEASURES AND THE SPECTRAL THEOREM, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 339-341, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50036-1.

K. Sundaresan and W.A. Woyczynski, L-ORTHOGONALLY SCATTERED MEASURES, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 343-350, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50037-3.

Charles Swartz, ABSOLUTELY SUMMING OPERATORS ON CX(S), In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 351-353, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50038-5.

T. Traynor, S-BOUNDED ADDITIVE SET FUNCTIONS, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 355-365, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50039-7.

Don H. Tucker and Stanley G. Wayment, SOME REMARKS ON THE NOTION OF “DERIVATIVES”, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 367-378, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50040-3.

J.J. Uhl Jr., A SURVEY OF MEAN CONVERGENCE OF MARTINGALES OF PETTIS INTEGRABLE FUNCTIONS1, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 379-385, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50041-5.

John N. Welch, ON THE CONSTRUCTION OF THE HILBERT SPACE L2,M FOR AN OPERATOR-VALUED MEASURE M, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 387-397, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50042-7.

, BIBLIOGRAPHY, In Vector and Operator Valued Measures and Applications, edited by Don H. Tucker and Hugh B. Maynard, Academic Press, 1973, Pages 399-458, ISBN 9780127024509, http://dx.doi.org/10.1016/B978-0-12-702450-9.50043-9.