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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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    $\begingroup$ Indicator function or characteristic function. You might have seen $\chi_A$. Anyway, $$\mathbf{1}_A(x) = \chi_A(x) = \begin{cases} 1 &, x \in A \\ 0 &, x \notin A.\end{cases}$$ $\endgroup$ – Daniel Fischer Dec 1 '14 at 19:56
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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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