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A basic course in measure and probability = theory for applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	A basic course in measure and probability/ Ross Leadbetter, Stamatis Cambanis, Vladas Pipiras.
其他題名:	theory for applications /
其他題名:	A Basic Course in Measure & Probability
作者:	Leadbetter, M. Ross.
其他作者:	Cambanis, Stamatis,
出版者:	Cambridge :Cambridge University Press, : 2014.,
面頁冊數:	xiv, 360 p. :ill., digital ; : 24 cm.;
標題:	Measure theory. -
電子資源:	https://doi.org/10.1017/CBO9781139103947
ISBN:	9781139103947

A basic course in measure and probability = theory for applications /
Leadbetter, M. Ross.

A basic course in measure and probabilitytheory for applications /[electronic resource] :A Basic Course in Measure & ProbabilityRoss Leadbetter, Stamatis Cambanis, Vladas Pipiras. - Cambridge :Cambridge University Press,2014. - xiv, 360 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9781139103947Subjects--Topical Terms:

527848
Measure theory.

LC Class. No.: QC20.7.M43 / L43 2014

Dewey Class. No.: 515.42

A basic course in measure and probability = theory for applications /
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100 1 $a Leadbetter, M. Ross. $3 1156717
245 1 2 $a A basic course in measure and probability $h [electronic resource] : $b theory for applications / $c Ross Leadbetter, Stamatis Cambanis, Vladas Pipiras.
246 3 $a A Basic Course in Measure & Probability
260 $a Cambridge : $b Cambridge University Press, $c 2014.
300 $a xiv, 360 p. : $b ill., digital ; $c 24 cm.
505 8 $a 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.
520 $a 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.
650 0 $a Measure theory. $3 527848
650 0 $a Probabilities. $3 527847
700 1 $a Cambanis, Stamatis, $d 1943-1995. $3 1156718
700 1 $a Pipiras, Vladas. $3 1156719
856 4 0 $u https://doi.org/10.1017/CBO9781139103947