Measure, Integration and a Primer on Probability Theory

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.