certain event

Noun

certain event (plural certain events)

1. An event that contains all of the possible outcomes and thus is known a priori to be certain to occur;
   • 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
   • 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...
2. (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).