What does the notation $1\{x\in Q\}$ stand for?

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While implementing Node Harvest I stumbled over the following notation in equation (1):

$$\hat{Y}(\mathbf{x}) = \sum_{g=1}^q \mu_g 1\{\mathbf{x} \in \mathcal{Q}_g\} \mathbf{w}_g$$

I assume the expression $1\{\mathbf{x} \in \mathcal{Q}_g\}$ evaluates to 1 if $\mathbf{x}$ is contained in $\mathcal{Q}_g$, and 0 otherwise.

If that is correct - what is the meaning of the slightly different notation in equation (2)? $$\mu_g = \frac{\sum_{i=1}^n 1\{\mathbf{X}_{i \dot{} \in \mathcal{Q}_g}\}\mathbf{Y}_i}{\sum_{i=1}^n 1\{\mathbf{X}_{i \dot{} \in \mathcal{Q}_g}\}}$$ What is the $\in \mathcal{Q}_g$ doing in the subscript of $\mathbf{X}$?