Proposition 5.3 . [034C]

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Proposition 5.3.

There exists $0<\alpha<1$ such that for all Borel subsets $K$ of $X$ , for all $j\in\mathbb{N}$ ,

\left[\alpha T_{\omega}(K)\right]^{\lambda^{j}}\leq T_{\omega}(f^{j}(K)).