Description 
1 online resource 
Series 
Wiley series in probability and statistics 

Wiley series in probability and statistics.

Contents 
Wiley Series in Probability and Statistics; Title Page; Copyright; Dedication; Preface; Acknowledgements; Chapter 1: Preliminary notions and definitions; 1.1 Sets of numbers; 1.2 Gambles; 1.3 Subsets and their indicators; 1.4 Collections of events; 1.5 Directed sets and MooreSmith limits; 1.6 Uniform convergence of bounded gambles; 1.7 Set functions, charges and measures; 1.8 Measurability and simple gambles; 1.9 Real functionals; 1.10 A useful lemma; Part I: Lower Previsions on Bounded Gambles; Chapter 2: Introduction; Chapter 3: Sets of acceptable bounded gambles; 3.1 Random variables 

3.2 Belief and behaviour3.3 Bounded gambles; 3.4 Sets of acceptable bounded gambles; Chapter 4: Lower previsions; 4.1 Lower and upper previsions; 4.2 Consistency for lower previsions; 4.3 Coherence for lower previsions; 4.4 Properties of coherent lower previsions; 4.5 The natural extension of a lower prevision; 4.6 Alternative characterisations for avoiding sure loss, coherence, and natural extension; 4.7 Topological considerations; Chapter 5: Special coherent lower previsions; 5.1 Linear previsions on finite spaces; 5.2 Coherent lower previsions on finite spaces 

5.3 Limits as linear previsions5.4 Vacuous lower previsions; 5.5 {0,1}valued lower probabilities; Chapter 6: nMonotone lower previsions; 6.1 nMonotonicity; 6.2 nMonotonicity and coherence; 6.3 Representation results; Chapter 7: Special nmonotone coherent lower previsions; 7.1 Lower and upper mass functions; 7.2 Minimum preserving lower previsions; 7.3 Belief functions; 7.4 Lower previsions associated with proper filters; 7.5 Induced lower previsions; 7.6 Special cases of induced lower previsions; 7.7 Assessments on chains of sets; 7.8 Possibility and necessity measures 

7.9 Distribution functions and probability boxesChapter 8: Linear previsions, integration and duality; 8.1 Linear extension and integration; 8.2 Integration of probability charges; 8.3 Inner and outer set function, completion and other extensions; 8.4 Linear previsions and probability charges; 8.5 The Sintegral; 8.6 The Lebesgue integral; 8.7 The Dunford integral; Chapter 9: Examples of linear extension; 9.1 Distribution functions; 9.2 Limits inferior; 9.3 Lower and upper oscillations; 9.4 Linear extension of a probability measure 

9.5 Extending a linear prevision from continuous bounded gambles9.6 Induced lower previsions and random sets; Chapter 10: Lower previsions and symmetry; 10.1 Invariance for lower previsions; 10.2 An important special case; 10.3 Interesting examples; Chapter 11: Extreme lower previsions; 11.1 Preliminary results concerning real functionals; 11.2 Inequality preserving functionals; 11.3 Properties of inequality preserving functionals; 11.4 Infinite nonnegative linear combinations of inequality preserving functionals; 11.5 Representation results 
Bibliography 
Includes bibliographical references and index 
Notes 
Print version record and CIP data provided by publisher 
Subject 
Games of chance (Mathematics)


Probabilities.


Statistical decision.

Form 
Electronic book

Author 
Cooman, Gert de.

LC no. 
2014004021 
ISBN 
0470723777 

1118761138 (ePub) 

1118762622 

1118762649 (Adobe PDF) 

9780470723777 

9781118761137 (ePub) 

9781118762622 

9781118762646 (Adobe PDF) 
