Measure, Integration and a Primer on Probability Theory: Volume 1 (Paperback, 2020)

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