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?

  • 1
    $\begingroup$ 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

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.