عنوان

A basic course in measure and probability :

1107020409

1107652529

9781107020405

9781107652521

dltt

A basic course in measure and probability :

[Book]

theory for applications /

Ross Leadbetter, University of North Carolina, Chapel Hill, Stamatis Cambanis, University of North Carolina, Chapel Hill, Vladas Pipiras, University of North Carolina, Chapel Hill

xiv, 360 pages :

illustrations ;

24 cm

Includes bibliographical references (page 356) and index

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, Lp-spaces; 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

8

"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 two-term course or for self-study. 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 'take-off point' for them as they specialize in areas that exploit mathematical machinery"--

Measure theory

Probabilities

Leadbetter, M. R.

Cambanis, Stamatis,1943-1995

Pipiras, Vladas

20150216232111.0

rda

[Book]

Y