Indicator variable syntax

Question

Are these syntax equivalent?

$$f(x,\lambda)=\lambda e^{-\lambda x}I_{(0,+\infty)}(x),\ \lambda > 0$$

$$f(x,\lambda) = \left \{ \begin{array}{cl} \lambda e^{-\lambda x} & x \gt 0 \\ 0 & \text{Otherwise} \end{array} \right .$$