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The RPF-Theorem

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2036)

Abstract

We now establish a version of Ruelle–Perron–Frobenius (RPF) Theorem along with a mixing property. Notice that this quite substantial fact is proved without any measurable structure on the space \(\mathcal{J}\). In particular, we do not address measurability issues of λ x and q x . In order to obtain this measurability we will need and we will impose a natural measurable structure on the space \(\mathcal{J}\). This will be done in the next chapter.

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Correspondence to Volker Mayer .

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© 2011 Springer-Verlag Berlin Heidelberg

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Mayer, V., Skorulski, B., Urbanski, M. (2011). The RPF-Theorem. In: Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry. Lecture Notes in Mathematics(), vol 2036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23650-1_3

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