I am sitting on an exercise. My prof gave me this function:
$$f(a) := \frac{1}{3} \cdot \textbf{1}_{(-\infty,\ 0]} (a) \frac{1}{2} e^{a/2} +\frac{2}{3} \cdot \textbf{1}_{(0,\ \infty]}(a) \frac{1}{5} e^{-a/5}$$
What the hell does this notation $\textbf{1}_{(-\infty,\ 0]}(a)$ mean?
It looks like an indicator function. The first time it appears it is 1 when a is on the interval (- $\infty$, 0] and zero otherwise. The second time it is 1 when a is positive, zero otherwise.