certain event

plural certain events

1. mathematicsAn event that contains all of the possible outcomes and thus is known a priori to be certain to occur;

   Hence the event A#95;1#92;capA#95;2#92;cap#92;dots#92;capA#95;k will be a certain event too, i.e. P(A#95;1#92;capA#95;2#92;cap#92;dots#92;capA#95;k)#61;1.

   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

   2 more examples

   Measure 0 is assigned to an impossible event, and measure 1 is assigned to a certain (sure) event. A certain event is denoted as #92;Omega; an impossible event, as #92;empty.

   1995, Michael Pecht, Product Reliability, Maintainability, and Supportability Handbook, CRC Press, page 17

   In probability theory, events are sets with a non-negative length that is at most one, since we assume that the sample space #92;Omega is the certain event and should be assigned the largest length, i.e., 1 (probability 100%).

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

2. 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).
   1. more formallymathematicsthe 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).