Lecture 1. D) Probability Space

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Probability Space

We call the ingredients needed to talk about probabilities the probability space.

A probability space is a triple [math](S,\mathcal{B},P)[/math], where [math]S[/math] is a sample space, [math]\mathcal{B}[/math] is a [math]\sigma[/math]-algebra of events in [math]S[/math], and [math]P[/math] is a probability function.
The interpretation:

  • [math]S[/math] is the set of possible singleton events.
  • [math]\mathcal{B}[/math] is the set of questions we can ask the probability function (like, what is the probability that this and that happens, but not that other thing).
  • [math]P[/math] maps sets into probabilities.