Del 125 i serien UNITEXT

Measure, Integration and a Primer on Probability Theory

Volume 1

Häftad, Engelska, 2020

779 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

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.

Produktinformation

Utgivningsdatum2020-12-01
Mått155 x 235 x 27 mm
Vikt788 g
FormatHäftad
SpråkEngelska
SerieUNITEXT
Antal sidor463
FörlagSpringer Nature Switzerland AG
ISBN9783030549398
ÖversättareSimon G. Chiossi

Tillhör följande kategorier

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.

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 σ-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.