Measure, Integration and a Primer on Proba...

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Beschreibung

The text contains detailed and complete proofs and includes instructive historical introductions to key chapters. These serve to illustrate the hurdles faced by the scholars that developed the theory, and allow the novice to approach the subject from a wider angle, thus appreciating the human side of major figures in Mathematics. The style in which topics are addressed, albeit informal, always maintains a rigorous character. The attention placed in the careful layout of the logical steps of proofs, the abundant examples and the supplementary remarks disseminated throughout all contribute to render the reading pleasant and facilitate the learning process. The exposition is particularly suitable for students of Mathematics, Physics, Engineering and Statistics, besides providing the foundation essential for the study of Probability Theory and many branches of Applied Mathematics, including the Analysis of Financial Markets and other areas of Financial Engineering.

Über den Autor

Stefano Gentili got his degree in Economics at Università Politecnica delle Marche, specialising in econometrics and financial markets analysis. He is currently manager in a town council of Marche region and he has authored two books concerning "finance in Italy's local governments". Among his main interests we can mention the econometric analysis of general systems, the development of forecasting models, the use of Mathematical Analysis tools for research and development in Economic Analysis.

Zusammenfassung

Interesting and enjoyable reading, even to a non expert readers

Each proposition presents clear and complete logical passages

Topics are introduced starting from simple concepts and then gradually go through more complex steps

Inhaltsverzeichnis

Part I Sets: 1 Round-up of topology.- 2 Types of sets.- Part II Borel sets and Baire functions on R: 3 Borel sets in R.- [...] functions on R.- 5 Borel functions and Baire functions.- Part III Families of sets: 6 Semi-algebras and algebras of sets .- 7. Monotone classes and ¿-algebras.- Part IV Measure theory: 8. Set functions and measure.- 9 The Lebesgue measure.- 10. Measurable functions.- Part V Theory of integration: 11 The Lebesgue integral.- 12 Comparing notions of integral.- Part VI Fundamental theorems of integral calculus: 13 Bounded variations and absolute continuity.- 14 Fundamental theorems of calculus for the Lebesgue integral.- Part VII Appendices: A Compact and totally bounded metric spaces.- B Urysohn's lemma and Tietze's theorem.

Details

Erscheinungsjahr:	2020
Fachbereich:	Analysis
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xi 463 S. 5 s/w Illustr. 16 farbige Illustr. 463 p. 21 illus. 16 illus. in color.
ISBN-13:	9783030549398
ISBN-10:	3030549399
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Gentili, Stefano
Übersetzung:	Chiossi, Simon G.
Auflage:	1st edition 2020
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 24 mm
Von/Mit:	Stefano Gentili
Erscheinungsdatum:	01.12.2020
Gewicht:	0,815 kg

Artikel-ID: 118554022