Measure theory
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Measure theory
Paid R. HalmosMeasure TheorySpringer-Verlag NewYork- Heidelberg • BerlinVA7* pdigrip camManaging Editorsp. R. IlalmosIndiana UniversityDepartment of M Measure theory MathematicsSwain Hall EastBloomington, Indiana 47401c. c. MooreUniversity of California at BerkeleyDepartment of MathematicsBerkeley, California 94720AMS Subject Classifications (1970)Primary: 28 - 02, 28A10, 28A15, 28A20, 28A25, 28A30, 28A35, 28A40, 28A60, 28A65,28A70Secondary: 60A05, 60BxxLibrary Measure theory of Congress Cataloging in Publication DataHalmos, Paul Richard, 1914-Measure theory.(Graduate texts in mathematics, 18)Reprint of the ed. published byMeasure theory
Van Nostrand, New York, in series: The University series in higher mathematics.Bibliography: p.1. Measure theory. I. Title. II, Series. [QA312.H26 19Paid R. HalmosMeasure TheorySpringer-Verlag NewYork- Heidelberg • BerlinVA7* pdigrip camManaging Editorsp. R. IlalmosIndiana UniversityDepartment of M Measure theory om Springer-Verlag.© 1950 by Litton Educational Publishing, Inc. and1974 by/Springer-Verlag New York Inc. Prixfed in the United States of America.ISBN 0-387-90088-8 Springer-Verlag New York Heidelberg Berlin ISBN 3-540-90088-8 Springer-Verlag Berlin Heidelberg New Yorkww*' pdígrip camPREFACEMy main Measure theory purpose in this book is to present a unified treatment of that part of measure theory which in recent years has shown itself to be most useful for itsMeasure theory
applications in modern analysis. If I have accomplished my purpose, then the book should be found usable both as a text for students and as a source Paid R. HalmosMeasure TheorySpringer-Verlag NewYork- Heidelberg • BerlinVA7* pdigrip camManaging Editorsp. R. IlalmosIndiana UniversityDepartment of M Measure theory places where my nomenclature differs from that in the existing literature of measure theory, I was motivated by an attempt to harmonize with the usage of other parts of mathematics. There are, for instance, sound algebraic reasons for using the terms “lattice” and “ring” for certain classes of sets— Measure theory reasons which are more cogent than the similarities that caused Hausdorff to use “ring” and “field.”The only necessary prerequisite for an intelligentMeasure theory
reading of the first seven chapters of this book is what is known in the United States as undergraduate algebra and analysis. For the convenience of Paid R. HalmosMeasure TheorySpringer-Verlag NewYork- Heidelberg • BerlinVA7* pdigrip camManaging Editorsp. R. IlalmosIndiana UniversityDepartment of M Measure theory of the words and symbols in the latter part of § 0 are defined only later, in the first seven chapters of the text, and that, accordingly, he should not be discouraged if, on first reading of § 0, he finds that he does not have the prerequisites for reading the prerequisites.At the end of almost ev Measure theory ery section there is a set of exercises which appear sometimes as questions but more usually as assertions that the reader is invited to prove. TheseMeasure theory
exercises should be viewed as corollaries to and sidelights on the results morePaid R. HalmosMeasure TheorySpringer-Verlag NewYork- Heidelberg • BerlinVA7* pdigrip camManaging Editorsp. R. IlalmosIndiana UniversityDepartment of MPaid R. HalmosMeasure TheorySpringer-Verlag NewYork- Heidelberg • BerlinVA7* pdigrip camManaging Editorsp. R. IlalmosIndiana UniversityDepartment of MGọi ngay
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