A probability measure is a mathematical function that assigns a numerical value to the likelihood of different outcomes in a random experiment. It is defined on a set of possible outcomes, known as a sample space, and must satisfy three key properties: non-negativity, normalization, and countable additivity. This means that the probability of any event is always between 0 and 1, the total probability of all possible outcomes equals 1, and the probability of the union of disjoint events equals the sum of their individual probabilities. In the context of measure theory, a probability measure is a specific type of measure that quantifies uncertainty. It is often used in fields such as statistics, finance, and science to model random phenomena. For example, in gambling, a probability measure can help determine the odds of winning a game, while in insurance, it can assess the risk of certain events occurring.