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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, University of North Carolina, Chapel Hill, Stamatis Cambanis, University of North Carolina, Chapel Hill, Vladas Pipiras, University of North Carolina, Chapel Hill.
其他題名:	theory for applications /
其他題名:	A Basic Course in Measure & Probability
作者:	Leadbetter, M.R,
其他作者:	Pipiras, Vladas,
面頁冊數:	1 online resource (xiv, 360 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
標題:	Probabilities. -
電子資源:	https://doi.org/10.1017/CBO9781139103947
ISBN:	9781139103947 (ebook)

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

A basic course in measure and probability :theory for applications /A Basic Course in Measure & ProbabilityRoss Leadbetter, University of North Carolina, Chapel Hill, Stamatis Cambanis, University of North Carolina, Chapel Hill, Vladas Pipiras, University of North Carolina, Chapel Hill. - 1 online resource (xiv, 360 pages) :digital, PDF file(s).

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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: 9781139103947 (ebook)Subjects--Topical Terms:

527847
Probabilities.

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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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 Probabilities. $3 527847
650 0 $a Measure theory. $3 527848
700 1 $a Pipiras, Vladas, $e author. $3 1440648
700 1 $a Cambanis, Stamatis, $d 1943-1995, $e author. $3 1440647
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856 4 0 $u https://doi.org/10.1017/CBO9781139103947