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