Erratum to 'Multifractal spectra of Birkhoff averages for a piecewise monotone interval map'(Fund. Math. 208 (2010), 95-121)

摘要

The proof of Theorem 10 in [1] is not correct. In [2] Lyapunov exponents for the Manneville Pomeau map T(x) = x + x~(1+s) mod 1 with 0 < s < 1 are considered. Examples of level sets La are given for which there exists a nonergodic invariant probability measure μ satisfying μ(log |T|) = a, h_μ = τ(a), and μ(L_a)= 0. Therefore, one has to expect that also the statement of Theorem 10 is wrong. However, the following weaker version of this theorem can be easily deduced from the proof of Proposition 9 in [1].