Introduction to Statistical Limit Theory. - Polansky, Alan M. (Chapman & Hall/CRC Texts in Statistical Science., 2011)
Sequences of Real Numbers and Functions Introduction Sequences of Real Numbers Sequences of Real Functions The Taylor Expansion Asymptotic Expansions Inversion of Asymptotic ExpansionsRandom Variables and Characteristic Functions Introduction Probability Measures and Random VariablesSome Important Inequalities Some Limit Theory for EventsGenerating and Characteristic FunctionsConvergence of Random Variables Introduction Convergence in ProbabilityStronger Modes of ConvergenceConvergence of Random Vectors Continuous Mapping Theorems Laws of Large Numbers The Glivenko-Cantelli TheoremSample Momen.