certain event

certain event (plural certain events)

1. (probability theory) An event that contains all of the possible outcomes and thus is known a priori to be certain to occur;
   (more formally) the entire sample space (which by definition has measure 1 and probability 1); said sample space with the exclusion of, at most, a set of measure 0 (thus retaining measure 1).
   • 1995, Michael Pecht, Product Reliability, Maintainability, and Supportability Handbook, CRC Press, page 17:

     Measure 0 is assigned to an impossible event, and measure 1 is assigned to a certain (sure) event. A certain event is denoted as ${\displaystyle \Omega }$; an impossible event, as ${\displaystyle \emptyset }$.

   • 2002, Andrew G. Bronevich; Alexander N. Karkishchenko, “The structure of fuzzy measure families induced by upper and lower probabilities”, in Carlo Bertoluzza; María Á. Gil; Dan A. Ralescu, editors, Statistical Modeling, Analysis and Management of Fuzzy Data, Springer, page 165:

     Hence the event ${\displaystyle A_{1}\cap A_{2}\cap \dots \cap A_{k}}$ will be a certain event too, i.e. ${\displaystyle P(A_{1}\cap A_{2}\cap \dots \cap A_{k})=1}$.

   • 2018, Athanasios Christou Micheas, Theory of Stochastic Objects, Taylor & Francis (CRC Press / Chapman & Hall), unnumbered page:

     In probability theory, events are sets with a non-negative length that is at most one, since we assume that the sample space ${\displaystyle \Omega }$ is the certain event and should be assigned the largest length, i.e., 1 (probability 100%).

• impossible event

• Event (probability theory) on Wikipedia.Wikipedia
• Measurable space on Wikipedia.Wikipedia
• σ-algebra on Wikipedia.Wikipedia