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Register a new userAccessible parts of the boundary for domains in metric measure spaces
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We prove in the setting of $Q$--Ahlfors regular PI--spaces the following result: if a domain has uniformly large boundary when measured with respect to the $s$--dimensional Hausdorff content, then its visible boundary has large $t$--dimensional Hausdorff content for every $0<t<sleq Q-1$. The visible boundary is the set of points that can be reached by a John curve from a fixed point $z_{0}in Omega$. This generalizes recent results by Koskela-Nandi-Nicolau (from $mathbb{R}^2$) and Azzam ($mathbb{R}^n$). In particular, our approach shows that the phenomenon is independent of the linear structure of the space.
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