Analysis and Probability

Klappentext Probability theory is a rapidly expanding field and is used in many areas of science and technology. Beginning from a basis of abstract analysis! this mathematics book develops the knowledge needed for advanced students to develop a complex understanding of probability. The first part of the book systematically presents concepts and results from analysis before embarking on the study of probability theory. The initial section will also be useful for those interested in topology! measure theory! real analysis and functional analysis. The second part of the book presents the concepts! methodology and fundamental results of probability theory. Exercises are included throughout the text! not just at the end! to teach each concept fully as it is explained! including presentations of interesting extensions of the theory. The complete and detailed nature of the book makes it ideal as a reference book or for self-study in probability and related fields. Zusammenfassung Probability theory is a rapidly expanding field and is used in many areas of science and technology. This book presents concepts and results from analysis before embarking on the study of probability theory. It also presents the concepts! methodology and fundamental results of probability theory.

Inhalt

Chapter 1: Elements of Set TheoryChapter 2: Topological PreliminariesChapter 3: Measure SpacesChapter 4: The IntegralChapter 5: Measures on Product -algebrasChapter 6: Elementary Notions in Probability TheoryChapter 7: Distribution Functions and Characteristic FunctionsChapter 8: Probabilities on Metric SpacesChapter 9: Central Limit ProblemChapter 10: Sums of Independent Random VariablesChapter 11: ConditioningChapter 12: Ergodicity, Mixing and Stationarity