A Note on the Ergodic Theorem

作者：de Carvalho Maria Pires^*; Moreira Fernando Jorge

来源：Qualitative Theory of Dynamical Systems, 2014, 13(2): 253-268.

DOI：10.1007/s12346-014-0116-x

• Birkhoff%26apos
• s averages
• Pointwise convergence

Given a space X, a sigma-algebra B on X and a measurable map T : X -%26gt; X, we say that a measure mu is half-invariant by T if, for any B is an element of B, we have mu (T-1(B)) %26lt;= mu(B). We will present a generalization of Birkhoff ergodic theorem to sigma-finite half-invariant measures.

• 出版日期2014-10