May 2014
Intermediate to advanced
258 pages
6h 11m
English
Content preview from Markov Chains: Analytic and Monte Carlo Computations
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A.3 Measure-theoretic framework
This appendix introduces without proofs the main notions and results in measure and integration theory, which allow to treat the subject of Markov chains in a mathematically rigorous way.
A.3.1 Probability spaces
A probability space 
is given by
- a set
encoding all possible random outcomes, - a
-field 
, which is a set constituted of certain subsets of 
, and satisfies
- the set
is in 
, - if
is in 
, then its complement 
is in , - if for in is in , then is in ,
- the set
- a probability ...
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