If $\Theta \in \mathbb{R}^d$ compact, $\rho(x,\theta): \mathbb{R}^p\times\Theta\rightarrow\mathbb{R}^+$ continuous in $\theta \in \Theta$ for all $x$, then $B=\{\rho(x,\theta), \theta \in \Theta\}=\{\rho_\theta(x), \theta \in \Theta\}$.

The excercise I am reading refers to $B$ as a "bracket," however I haven't able to find much more about it, probably because of the generic name. It is used in this exercise in relation to the law of large numbers.

  • $\begingroup$ Do you mean $\rho: \mathbb{R}^p \times \Theta \to \mathbb{R}^+$? $\endgroup$ – Randall Oct 19 '17 at 0:40
  • $\begingroup$ @Randall Yes, it was a typo. $\endgroup$ – Cure Oct 19 '17 at 0:49

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