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I understand everything in this document on the first page except the following:

\begin{align} \overline{\int_a^b}f&=\inf\left\{\int_a^b\psi:\psi\geqslant f,\psi=\sum_{j=1}^nc_j\mathbb{1}_{\left(x_{j-1},x_j\right]}\right\}. \end{align}

What does "$1_{\left(x_{j-1},x_j\right]}$" mean? Why is there a "$1$"?

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1 Answer 1

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it is an indicator function, which is $1$ if $x \in (x_{j-1},x_j]$ and 0 otherwise.

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