Certain event
"Certain event" in a Sentence (3 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.
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.
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%).