Probability measure

In probability theory, a probability measure for the mathematical description of a probability distribution is used. A probability is a function which assigns to each event from the amount of a random number between an experiment and called probability, and has the following properties:

• The certain event has a probability.
• The probability that at least one of a plurality disjoint events occurs is equal to the sum of the probabilities of these events.

Definition

Be a measurable space, ie a σ - algebra over the base amount. A probability measure is a function that satisfies the following Kolmogorov axioms:

• Normalization:
• σ - additivity: For every sequence of pairwise disjoint sets from ( so if follows ) applies

A probability measure is a measure on a measurement space with the property. The combination of result set event algebra and probability measure, ie the measure space is called a probability space.