Weak Convergence of Measures: Applications in Probability (CBMS-NSF Regional Conference Series in Applied Mathematics, Series Number 5)

Annotation A treatment of the convergence of probability measures from the foundations to applications in limit theory for dependent random variables. Mapping theorems are proved via Skorokhod's representation theorem; Prokhorov's theorem is proved by construction of a content. The limit theorems at the conclusion are proved under a new set of conditions that apply fairly broadly, but at the same time make possible relatively simple proofs Weak Convergence of Measures:Applications in Probability......Page 1 Contents......Page 8 Preface......Page 10 1. Introduction.......Page 12 2. Weak convergence.......Page 13 3. Random elements and convergence in distribution.......Page 17 4. Prokhorov's theorem.......Page 20 5. The space......Page 23 6. A maximal inequality.......Page 27 7. Tightness.......Page 31 8. Limit theorems.......Page 34 BIBLIOGRAPHY......Page 39