Probability Space

Let be a set and a sigma-algebra on it.
Let .
Suppose:

• is a Measure on
• 
  Then is a probability space.
  Equivalently:
  A Measure Space is called a probability space if .

The function is called Probability Measure

Probability space provides a model for an experiment
whose outcome is subjective to chance.
The interpretation is as follows:

• is the set of possible outcomes
• is the set of observable sets of outcomes or events
• is the probability of the event .

In addition to measure theory,
probability theory also has the notion of Independence.