Following up on this question: Definition of an "Experiment" in Probability
According to Wikipedia, an experiment is a procedure that can be infinitely repeated and has a set of possible outcomes. Why should we care if the experiment can be infinitely repeated?
An experiment is modeled as a probability space with each outcome being a point in the sample space. There's nothing in the definition of a probability space that indicates that the experiment should be infinitely repeatable. Even an experiment that hypothetically can only be repeated a finite number of times could be correctly modeled as a probability space, regardless of whether its sample space is finite or not.
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