Definition 1.2 . [01XF]

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Definition 1.2.

For $x\in X$ we define the regularity scale $r_{x}$ by

\displaystyle r_{x}\equiv\max_{0<r\leq 1}\big\{\sup_{B_{r}(x)}|{\rm Rm}|\leq r^{-2}\big\}\,.

(1.5)

If $x\in\mathcal{S}$ is in the singular set of $X$ , then $r_{x}\equiv 0$ .