<p>I am following an IO paper and, at some point, a function <span class="math-container">$h(\cdot)\in \mathbb{R}^2_+$</span> is defined as</p>
<p><span class="math-container">$$h(t) = \cases{\mathbb{1}(t=k)*|\mathbb{N}(0,1)|\\\mathbb{1}(t&lt;k)*|\mathbb{N}(0,1)|}$$</span> where <span class="math-container">$k\in\mathbb{N}$</span> is given. I had never seen the &quot;<span class="math-container">$*|\mathbb{N}(0,1)|$</span>&quot; part. Is it just the absolute value of one sample drawn from a standard normal?</p>

CC BY-SA 4.0
2022-12-27T17:19:00.760Z
But what is $\mathbb{1}$? In mathematics, usually, it is the  *indicator function* of a set.
BakerStreet
CC BY-SA 4.0
2022-12-27T18:10:10.660Z
@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
1muflon1
CC BY-SA 4.0
2022-12-27T18:15:45.847Z
I don't mean  the $\mathbb{N}$, even if it is strange, I mean the big $\mathbb{1}$, the $1$ written in mathbb.
BakerStreet
CC BY-SA 4.0
2022-12-27T18:26:56.603Z
The symbol $|.|$can  mean also the cardinality of a set, but without reading the paper it is a mistery.
BakerStreet
<definition><industrial-organisation><probability>
What does this notation mean?
marcvaliente
# What does this notation mean?

(Asked by: username_0 on 2022-12-27)

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 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?

**Tags:** definition, industrial-organisation, probability
> **Comments:**
> **username_1**: But what is $\mathbb{1}$? In mathematics, usually, it is the  *indicator function* of a set.  
> **username_2**: @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  
> **username_1**: I don't mean  the $\mathbb{N}$, even if it is strange, I mean the big $\mathbb{1}$, the $1$ written in mathbb.  
> **username_1**: The symbol $|.|$can  mean also the cardinality of a set, but without reading the paper it is a mistery.  

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## 0 answers

