 Then  "X"  is an "almost surely constant random variable" if there exists formula_2 such that
and is furthermore a "constant random variable" if

Note that a constant random variable is almost surely constant, but not necessarily "vice versa", since if  "X"  is almost surely constant then there may exist  γ ∈ Ω  such that  "X"(γ) ≠ "k"0  (but then necessarily Pr({γ}) = 0, in fact Pr(X ≠ "k"0) = 0).For practical purposes, the distinction between  "X"  being constant or almost surely constant is unimportant, since the cumulative distribution function  "F"("x")  of  "X"  does not depend on whether  "X"  is constant or 'merely' almost surely constant.In either case,
The function  "F"("x")  is a step function; in particular it is a translation of the Heaviside step function.