The validity space of Dunford-Schwartz ergodic theorem for infinite measure

Abstract

We show that if $(\Omega ,\mu )$ is an infinite measure space, the pointwise Dunford-Shwartz ergodic theorem holds for $f\in {\mathcal{L}}^1(\Omega )+{\mathcal{L}}^{\infty }(\Omega )$ if and only if $\mu \{f>\lambda \}<\infty$ for all $\lambda >0$.

arXiv commentThere is an error in the last section of the article

References in corpus (1)

• Pointwise ergodic theorems in symmetric spaces of measurable functions