Abstract
We show that if a σ-finite infinite measure space (Ω,μ) is quasi-non-atomic, then the Dunford–Schwartz pointwise ergodic theorem holds for f∈L1(Ω)+L∞(Ω) if and only if μ{|f|≥λ}<∞ for all λ>0.
Original language | English (US) |
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Pages (from-to) | 234-247 |
Number of pages | 14 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 461 |
Issue number | 1 |
DOIs | |
State | Published - May 1 2018 |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics