說明 
xiv, 360 pages : illustrations ; 24 cm 

text rdacontent 

unmediated rdamedia 

volume rdacarrier 
附註 
"Originating from the authors' own graduate course at the University of North Carolina, this material has been thoroughly tried and tested over many years, making the book perfect for a twoterm course or for selfstudy. It provides a concise introduction that covers all of the measure theory and probability most useful for statisticians, including Lebesgue integration, limit theorems in probability, martingales, and some theory of stochastic processes. Readers can test their understanding of the material through the 300 exercises provided. The book is especially useful for graduate students in statistics and related fields of application (biostatistics, econometrics, finance, meteorology, machine learning, and so on) who want to shore up their mathematical foundation. The authors establish common ground for students of varied interests which will serve as a firm 'takeoff point' for them as they specialize in areas that exploit mathematical machinery" Provided by publisher 

Machine generated contents note: Preface; Acknowledgements; 1. Point sets and certain classes of sets; 2. Measures: general properties and extension; 3. Measurable functions and transformations; 4. The integral; 5. Absolute continuity and related topics; 6. Convergence of measurable functions, Lpspaces; 7. Product spaces; 8. Integrating complex functions, Fourier theory and related topics; 9. Foundations of probability; 10. Independence; 11. Convergence and related topics; 12. Characteristic functions and central limit theorems; 13. Conditioning; 14. Martingales; 15. Basic structure of stochastic processes; References; Index 

Includes bibliographical references (page 356) and index 
主題 
Measure theory


Probabilities


MATHEMATICS / Probability & Statistics / General. bisacsh


Maßtheorie. gnd


Wahrscheinlichkeitsrechnung. gnd


Wahrscheinlichkeitstheorie. gnd


Lehrnbuch

Alt Author 
Cambanis, Stamatis, 19431995, author


Pipiras, Vladas, author

