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

Record Type:	Language materials, printed : Monograph/item
Title/Author:	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.
Reminder of title:	theory for applications /
remainder title:	A Basic Course in Measure & Probability
Author:	Leadbetter, M.R,
other author:	Cambanis, Stamatis,
Description:	1 online resource (xiv, 360 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Measure theory. -
Online resource:	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:

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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020 $a 9781139103947 (ebook)
020 $z 9781107020405 (hardback)
020 $z 9781107652521 (paperback)
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100 1 $a Leadbetter, M.R, $e author. $3 1440646
245 1 2 $a A basic course in measure and probability : $b theory for applications / $c Ross Leadbetter, University of North Carolina, Chapel Hill, Stamatis Cambanis, University of North Carolina, Chapel Hill, Vladas Pipiras, University of North Carolina, Chapel Hill.
246 3 $a A Basic Course in Measure & Probability
264 1 $a Cambridge : $b Cambridge University Press, $c 2014.
300 $a 1 online resource (xiv, 360 pages) : $b digital, PDF file(s).
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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, $e author. $3 1440647
700 1 $a Pipiras, Vladas, $e author. $3 1440648
776 0 8 $i Print version: $z 9781107020405
856 4 0 $u https://doi.org/10.1017/CBO9781139103947