From [1], on page 9, one can find the following expression.
$$L:\mathbb{R}\setminus\mathcal{A}\rightarrow\mathbb{R}_{++}$$
What is $\mathbb{R}_{++}$ is meant to be?
The $\mathbb{R}_{+}$ symbol seems to usually mean positive real numbers or non-negative real numbers, but I've never seen (and cannot find anything) about $\mathbb{R}_{++}$.
[1] – Beck, Amir and Shoham Sabach. “Weiszfeld’s Method: Old and New Results.” Journal of Optimization Theory and Applications 164 (2015): 1-40. https://doi.org/10.1007/s10957-014-0586-7
Best Answer
The full quote is:
On page 4 of the same paper, the authors note that $\omega_i > 0$ for all $i=1,2,\dotsc,m$, from which it follows that each summand in (12) must be positive, and so $L(x) > 0$ for any $x\not\in\cal{A}$. Given this context, it seems that the notation $\mathbb{R}_{++}$ is meant to denote the open half-line, i.e. $\mathbb{R}_{++} = (0,\infty)$. One suspects that the authors are simply trying to emphasize that $L(x)$ is strictly positive, and cannot ever be zero.