Real Analysis and Probability.(Cambridge Studies in Advanced Mathematics Vol. 74) hardcover 512 p.
Dudley, R.M. 著
内容
目次
1. Foundations: set theory; 2. General topology; 3. Measures; 4.Integration; 5. Lp spaces: introduction to functional analysis; 6. Convexsets and duality of normed spaces; 7. Measure, topology, and differentiation;8. Introduction to probability theory; 9. Convergence of laws and centrallimit theorems; 10. Conditional expectations and martingales; 11. Convergenceof laws on separable metric spaces; 12. Stochastic processes; 13.Measurability: Borel isomorphism and analytic sets; Appendixes: A. Axiomaticset theory; B. Complex numbers, vector spaces, and Taylor's theorem withremainder; C. The problem of measure; D. Rearranging sums of nonnegativeterms; E. Pathologies of compact nonmetric spaces; Indices.
