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gentili stefano - measure, integration and a primer on probability theory
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Measure, Integration and a Primer on Probability Theory Volume 1




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 12/2020
Edizione: 1st ed. 2020





Trama

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.







Sommario

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.-  4.Baire 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 s-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.  




Autore

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.











Altre Informazioni

ISBN:

9783030549398

Condizione: Nuovo
Collana: UNITEXT
Dimensioni: 235 x 155 mm
Formato: Brossura
Illustration Notes:XI, 463 p. 21 illus., 16 illus. in color.
Pagine Arabe: 463
Pagine Romane: xi
Traduttore: Chiossi, Simon G.


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