A probability distribution is called a degenerate distribution if it is 1 at a point, 0 elsewhere.
A distribution is also degenerate if:
f(x)=\begin{cases} 1 & x=\theta \ 0, & \text{others} \end{cases}
2. $$ F(x) = \begin{cases} 0, & x<\theta \\ 1, & x\geq \theta \end{cases}