A probability space is a triple , where is a sample space, is a sigma-algebra of events and is a probability measure on .
The three building blocks of a probability space can be described as follows:
the sample space is the set of all possible outcomes of a probabilistic experiment;
the sigma-algebra is the set of all subsets of that are considered events;
the probability measure is a function that associates a probability to each of the events belonging to the sigma-algebra .
Suppose the probabilistic experiment consists in extracting a ball from an urn containing two balls, one red () and one blue ().
The sample space is
A possible sigma-algebra of events iswhere the event (the empty set) could be described as "nothing happens", the event could be described as "either a blue ball or a red ball is extracted", the event could be described as "a red ball is extracted", and the event could be described as "a blue ball is extracted".
A possible probability measure on is
The lecture entitled Probability contains a more detailed explanation of the concept of probability space and of the properties that must be satisfied by its building blocks.
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