Real analysis and probability
R.M. Dudley.
Cambridge ; New York : Cambridge University Press, 2002.
x, 555 págs. ; 24 cm.
Serie: Cambridge studies in advanced mathematics ; 74
ISBN: 052180972X (hardback), 0521007542 (pbk.)
Reimpresión revisada del original publicado por Wadsworth & Brooks/Cole en 1989.
Incluye referencias bibliográficas e índices.
Reseña: MathSciNet, 2003h:60001
Contenido
- 1. Foundations; set theory
- 2. General topology
- 3. Measures
- 4. Integration
- 5. Lp spaces; introduction to functional analysis
- 6. Convex sets and duality of normed spaces
- 7. Measure, topology, and differentiation
- 8. Introduction to probability theory
- 9. Convergence of laws and central limit theorems
- 10. Conditional expectations and martingales
- 11. Convergence of laws on separable metric spaces
- 12. Stochastic processes
- 13. Measurability: Borel isomorphism and analytic sets
- Appendixes: A. Axiomatic set theory
- B. Complex numbers, vector spaces, and Taylor's theorem with remainder
- C. The problem of measure
- D. Rearranging sums of nonnegative terms
- E. Pathologies of compact nonmetric spaces.
