Measures, integrals and martingales

Cover; Half-title; Title; Copyright; Contents; Prelude; 1 Prologue; 2 The pleasures of counting; 3 Sigma-algebras; 4 Measures; 5 Uniqueness of measures; 6 Existence of measures; 7 Measurable mappings; 8 Measurable functions; 9 Integration of positive functions; 10 Integrals of measurable functions and null sets; 11 Convergence theorems and their applications; 12 The function spaces ... ; 13 Product measures and Fubini's theorem; 14 Integrals with respect to image measures; 15 Integrals of images and Jacobi's transformation rule; 16 Uniform integrability and Vitali's convergence theorem.
A concise undergraduate introduction to contemporary measure and integration theory as it is needed in many parts of analysis and probability.