Multifunctions and Integrands Stochastic Analysis, Approximation and

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1091 Multifunctions and Integrands Stochastic Analysis, Approximation and Optimization Proceedings of a Conference held in Catania, Italy, June 7-16, 1983

Edited by G. Salinetti

Springer-Verlag Berlin Heidelberg New York Tokyo 1984

Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann

1091 Multifunctions and Integrands Stochastic Analysis, Approximation and Optimization Proceedings of a Conference held in Catania, Italy, June 7-16, 1983

Edited by G. Salinetti

Springer-Verlag Berlin Heidelberg New York Tokyo 1984

Editor

Gabriella Salinetti Dipartimento di Statistica, Probabilita e Statistic he Applicate Universita di Roma "La Sapienza" 00100 Roma - Italy

AMS Subject Classification (1980): 50-XX, 49-XX, 93EXX, 52A22, 28-XX ISBN 3-540-13882-X Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-13882-X Springer-Verlag New York Heidelberg Berlin Tokyo Library of Congress Cataloging in Publication Data. Main entry under title: Multifunctions and integrands. (Lecture notes in mathematics; 1091) Sponsored jointly by the Dipartimento di statistics, probabilita e statistiche applicate of the Universita "La Sapienza" di Roma and the Seminario matematico, Universita di Catania. Bibliography: p.1. Stochastic analysis-Congresses. 2. Approximation theory-Congresses. 3. Mathematical optimization-Congresses. I. Salinetti, G. (Gabriella), 1946-. II. Universita degli studi di Roma "La Sapienza": Dipartimento di statistica, probabilita e statistiche applicate. III. Universita di Catania. Seminario matematico. IV. Series: Lecture notes in mathematics (Springer-Verlag); 1091. 0A3.L28 no. 1091 510 s 84-23565 [0A274.2J [519.2J ISBN 0-387-13882-X (U.S.) This work IS subject to copyright. All nghts are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.

© by Springer-Verlag Berlin Heidelberg 1984 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210

PREFACE

This publication presents the Broceedings of the international conference on "MULTIFUNCTIONS AND INTEnRANDS: Stochastic Analysis, Approximation and Optimization" held in Catania, Italy, in June 1983 under the scientific direction of R.T. Rockafellar, M. Valadier and G. Sal.Lnet t.L, The purpose of the conference

was

to

survey

the current state of the

art, report on recent progress and delineate further directions of research with special attention to applications. Modern applications in statistics, probability, operation research, physics and economics have

focused

attention on situations and rrathematical mode'ls

where solutions are not necessarily unique, feasible sets depend - often measurably - on parameters, perturbations play a crucial role, functions have lost their "traditiona

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