Title: Measures, integrals and martingales /
Authors: Schilling, René L.
Date: 2017
Publisher: Cambridge University Press,
Physical description: 1 volume : illustrations (black and white) ; 25 cm
Language: English
LC classification: Q
Contents: List of symbols -- Prelude -- Dependence chart -- Prologue -- The pleasures of counting -- ð-Algebras -- Measures -- Uniqueness of measures -- Existence of measures -- Measurable mappings -- Measurable functions -- Integration of positive functions -- Integrals of measurable functions -- Null sets and the 'almost everywhere' -- Convergence theorems and their applications -- The function spaces [cursive capital L, superscript p] -- Product measures and Fubini's theorem -- Integrals with respect to image measures -- Jacobi's transformation theorem -- Dense and determining sets -- Hausdorff measure -- The Fourier transform -- The Radon-Nikodým theorem -- Riesz representation theorems -- Uniform integrability and Vitali's convergence theorem -- Martingales -- Martingale convergence theorems -- Martingales in action -- Abstract Hilbert spaces -- Conditional expectations -- Orthonormal systems and their convergence behaviour -- Appendix A : lim inf and lim sup -- Appendix B : Some facts from topology -- Appendix C : The volume of a parallelepiped -- Appendix D : The integral of complex-valued functions -- Appendix E : Measurability of the continuity points of a function -- Appendix F : Vitali's covering theorem -- Appendix G : Non-measurable sets -- Appendix H : Regularity of measures -- Appendix I : A summary of the Riemann integral.
Notes: Previous edition: 2005.
Subject headings (LCSH): Integrals.; Martingales (Mathematics); Measure theory.