Borel sets in \(\mathbb {R}\)
Open and closed subsets of \(\mathbb {R}\) are but special families of sets in a larger class, that of Borel sets. In this Chapter with the aid of the principle of transfinite induction, we will obtain the main properties of Borel classes and uncover the
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Stefano Gentili
Measure, Integration and a Primer on Probability Theory Volume 1
UNITEXT - La Matematica per il 3+2 Volume 125
Editor-in-Chief Alfio Quarteroni, Politecnico di Milano, Milan, Italy; EPFL, Lausanne, Switzerland Series Editors Luigi Ambrosio, Scuola Normale Superiore, Pisa, Italy Paolo Biscari, Politecnico di Milano, Milan, Italy Ciro Ciliberto, Università di Roma “Tor Vergata”, Rome, Italy Camillo De Lellis, Institute for Advanced Study, Princeton, NJ, USA Massimiliano Gubinelli, Hausdorff Center for Mathematics, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany Victor Panaretos, Institute of Mathematics, EPFL, Lausanne, Switzerland
The UNITEXT - La Matematica per il 3+2 series is designed for undergraduate and graduate academic courses, and also includes advanced textbooks at a research level. Originally released in Italian, the series now publishes textbooks in English addressed to students in mathematics worldwide. Some of the most successful books in the series have evolved through several editions, adapting to the evolution of teaching curricula. Submissions must include at least 3 sample chapters, a table of contents, and a preface outlining the aims and scope of the book, how the book fits in with the current literature, and which courses the book is suitable for. For any further information, please contact the Editor at Springer: francesca. [email protected] THE SERIES IS INDEXED IN SCOPUS
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Stefano Gentili
Measure, Integration and a Primer on Probability Theory Volume 1
123
Stefano Gentili Funzionario Dirigente P.A. Tolentino, Macerata, Italy Translated by Simon G. Chiossi Departamento de Matemática Aplicada Universidade Federal Fluminense Niterói, Rio de Janeiro, Brazil
ISSN 2038-5714 ISSN 2532-3318 (electronic) UNITEXT - La Matematica per il 3+2 ISSN 2038-5722 ISSN 2038-5757 (electronic) ISBN 978-3-030-54939-8 ISBN 978-3-030-54940-4 (eBook) https://doi.org/10.1007/978-3-030-54940-4 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at t
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