Abstract
In [V] the third author studied statistical properties of words generated by dynamical sources by using generalized Ruelle operators. This erratum aims to show that a supplementary condition should be added in Definition 2.1 of dynamical sources. This supplementary condition (called (d4) below) is closely related to the so-called Bounded Distortion Property and should be used at two different stages of the paper: first in the definition of the generalized operator G s, second in the proof of Proposition 2 that deals with the Positivity Theorem of Krasnoselskii. We also prove that this condition is actually necessary and provide an example of a source which does not satisfy condition (d4) and for which G s is not well-defined.
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Chazal, F., Maume-Deschamps, V. & Vallée, B. Erratum to “Dynamical Sources in Information Theory: Fundamental Intervals and Word Prefixes”. Algorithmica 38, 591–596 (2004). https://doi.org/10.1007/s00453-003-1057-y
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DOI: https://doi.org/10.1007/s00453-003-1057-y