Bold 1 with interval as subscript in function definition - what does it mean?

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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?

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1 Answer

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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.

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