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I am following an IO paper and, at some point, a function $h(\cdot)\in \mathbb{R}^2_+$ is defined as

$$h(t) = \cases{\mathbb{1}(t=k)*|\mathbb{N}(0,1)|\\\mathbb{1}(t<k)*|\mathbb{N}(0,1)|}$$ where $k\in\mathbb{N}$ is given. I had never seen the "$*|\mathbb{N}(0,1)|$" part. Is it just the absolute value of one sample drawn from a standard normal?

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  • $\begingroup$ But what is $\mathbb{1}$? In mathematics, usually, it is the indicator function of a set. $\endgroup$
    – BakerStreet
    Dec 27, 2022 at 17:19
  • $\begingroup$ @BakerStreet if its a distribution 0 would be the mean and 1 variance, but indeed it is a bit weird notation. Usually you would not use the same N for normal as for natural set of numbers $\endgroup$
    – 1muflon1 ♦
    Dec 27, 2022 at 18:10
  • $\begingroup$ I don't mean the $\mathbb{N}$, even if it is strange, I mean the big $\mathbb{1}$, the $1$ written in mathbb. $\endgroup$
    – BakerStreet
    Dec 27, 2022 at 18:15
  • $\begingroup$ The symbol $|.|$can mean also the cardinality of a set, but without reading the paper it is a mistery. $\endgroup$
    – BakerStreet
    Dec 27, 2022 at 18:26

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