What is the meaning of $\mathbb{R}_{++}$? 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
 A: The full quote is:

Another observation, which appears in Kuhn and Kuenne [12], is that Weiszfeld’s
  method is, in fact, a gradient method. Indeed, a simple computation shows that an
  alternative representation of the operator $T$ is given by
  $$ \renewcommand{\vec}[1]{\mathbf{#1}}
T(\vec{x}) = \vec{x} - \frac{1}{L(\vec{x})} \nabla f(\vec{x}) \qquad(\vec{x}\not\in\cal{A}), \tag{11} $$
  where the operator $L:\mathbb{R}^d\setminus\cal{A} \to \mathbb{R}_{++}$ is defined by
  $$ L(\vec{x}) := \sum_{i=1}^{m} \frac{\omega_i}{\|\vec{x}-\vec{a}_i\|}. \tag{12} $$

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. 
