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A basic course in measure and probability[electronic resource] :theory for applications /

紀錄類型:	書目-電子資源 : Monograph/item
杜威分類號:	515.42
書名/作者:	A basic course in measure and probability : theory for applications // Ross Leadbetter, Stamatis Cambanis, Vladas Pipiras.
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.
標題:	Probabilities.
ISBN:	9781139103947
ISBN:	9781107020405
ISBN:	9781107652521
內容註:	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.
摘要、提要註:	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 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.
電子資源:	https://doi.org/10.1017/CBO9781139103947

A basic course in measure and probability[electronic resource] :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:

495639
Measure theory.

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

Dewey Class. No.: 515.42

A basic course in measure and probability[electronic resource] :theory for applications /
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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 495639
650 0 $a Probabilities. $3 171876
700 1 $a Cambanis, Stamatis, $d 1943-1995. $3 711295
700 1 $a Pipiras, Vladas. $3 711296
856 4 0 $u https://doi.org/10.1017/CBO9781139103947