![]() ![]() Semirings and Algebras of Sets Measures on Semirings Outer Measures and Measurable Sets The Outer Measure Generated by a Measure Measurable Functions Simple and Step Functions The Lebesgue Measure Convergence in Measure Abstract Measurability The Stone-Weierstrass Approximation Theorem Topological Spaces Continuous Real-Valued Functions Separation Properties of Continuous Functions I I. 7.Įlementary Set Theory Countable and Uncountable Sets The Real Numbers Sequences of Real Numbers The Extended Real Numbers Metric Spaces Compactness in Metric Spaces Printed in the United States of America 98 99 00 0 IįUNDAMENTALS OF REAL ANALYSIS 1. ![]() Includes bibliographical references and index. Library of Congress Cataloging-in-Publication Data Aliprantis, Charalambos D. ACADEMIC PRESSĥ25 B Street, Suite 1900, San Diego, California 92101-4495, USA ACADEMIC PRESS LIMITED 24-28 Oval Road, London NWI 7DX, UK No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Purdue University, IndianapolisĪCADEMIC PRESS San Diego London Boston New York Sydney Tokyo Toronto OWEN BURKINSHAW Department of Mathematical Sciences Indiana University. ALIPRANTIS Departments of Economics and Mathematics Purdue University and PRINCIPLES OF REAL ANALYSIS Third EditionĬHARALAMBOS D.
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