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Analysis and Probability

Publisher: 
Elsevier
Number of Pages: 
448
Price: 
150.00
ISBN: 
9780124016651
Date Received: 
Wednesday, August 14, 2013
Reviewable: 
No
Include In BLL Rating: 
No
Aurel Spǎtaru
Series: 
Elsevier Insights
Publication Date: 
2013
Format: 
Hardcover
Category: 
Textbook

Analysis and Probability, 1st Edition

Chapter 1: Elements of Set Theory
1.1 Sets and operations on sets
1.2 Functions and Cartesian products
1.3 Equivalent relations and partial orderings


Chapter 2: Topological Preliminaries
2.1 Construction of some topological spaces
2.2 General properties of topological spaces
2.3 Metric spaces


Chapter 3: Measure Spaces
3.1 Measurable spaces
3.2 Measurable functions
3.3 Denitions and properties of the measure
3.4 Extending certain measures


Chapter 4: The Integral
4.1 Denitions and properties of the integral
4.2 Radon-Nikodým theorem and the Lebesgue decomposition
4.3 The spaces Lp
4.4 Convergence for sequences of measurable functions


Chapter 5: Measures on Product -algebras
5.5 The product of a finite number of measures
5.6 The product of an infnite number of measures


PART TWO: PROBABILITY
Chapter 6: Elementary Notions in Probability Theory
6.1 Events and random variables
6.2 Conditioning and independence


Chapter 7: Distribution Functions and Characteristic Functions
7.1 Distribution functions
7.2 Characteristic functions


Chapter 8: Probabilities on Metric Spaces
8.1 Probabilities in a metric space
8.2 Topology in the space of probabilities


Chapter 9: Central Limit Problem
9.1 Infnitely divisible distribution/characteristic functions
9.2 Convergence to an infnitely divisible distribution/characteristic function


Chapter 10: Sums of Independent Random Variables
10.1 Weak laws of large numbers
10.2 Series of independent random variables
10.3 Strong laws of large numbers
10.4 Laws of the iterated logarithm


Chapter 11: Conditioning
11.1 Conditional expectations, conditional probabilities and conditional independence
11.2 Stopping times and semimartingales


Chapter 12: Ergodicity, Mixing and Stationarity
12.1 Ergodicity and mixing
12.2 Stationary sequences

 

Publish Book: 
Modify Date: 
Wednesday, August 14, 2013

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