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arXiv · 1503.00749

Projective distance and $g$-measures

Liliana Trejo-Valencia·Edgardo Ugalde
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Abstract

We introduce a distance in the space of fully-supported probability measures on one-dimensional symbolic spaces. We compare this distance to the $\bar{d}$-distance and we prove that in general they are not comparable. Our projective distance is inspired on Hilbert's projective metric, and in the framework of $g$-measures, it allows to assess the continuity of the entropy at $g$-measures satisfying uniqueness. It also allows to relate the speed of convergence and the regularity of sequences of locally finite $g$-functions, to the preservation at the limit, of certain ergodic properties for the associate $g$-measures.

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Liliana Trejo-Valencia, Edgardo Ugalde. 2015-03-02. Projective distance and $g$-measures. https://arxiv.org/abs/1503.00749

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