Individual ergodic theorems for infinite measure
Individual ergodic theorems for infinite measure
Given a $\sigma $-finite infinite measure space $(\Omega ,\mu )$, it is shown that any Dun\-ford–Schwartz operator $T: \mathcal {L}^1(\Omega )\to \mathcal {L}^1(\Omega )$ can be uniquely extended to the space $\mathcal {L}^1(\Omega )+\mathcal {L}^\infty (