Probability Space

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, the probability space, or probability triple, is a concept which serves as a rigorous mathematical ground for the conventional idea of randomness. It is a mathematical model of a real-world situation (or "experiment") where we recognize that certain things occur "at random". The model works as following: first, at the outset of the experiment we attempt to envision all possible outcomes which might possibly happen, the set of all such outcomes is called the sample space ¿. Second, we recognize that the elementary outcomes could be too little of practical use, and that the more complicated events, consisting possibly of many different elementary outcomes, are of more interest. The collection of all such events is called the ¿-algebra scriptstyle mathcal{F}. Third, we have to specify how likely one or another event is going to happen, which is done using the probability measure function P. These three components scriptstyle (Omega,; mathcal{F},; P) together constitute the probability space - hence the name "triple".