A general local ergodic theorem in \(L_ 1\) (Q1067183)
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scientific article; zbMATH DE number 3927686
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A general local ergodic theorem in \(L_ 1\) |
scientific article; zbMATH DE number 3927686 |
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A general local ergodic theorem in \(L_ 1\) (English)
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1985
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Let \(\{T_ t\}_{t>0}\) be a strongly continuous semi group of linear contractions on the \(L_ 1\) space of a measure space (X,\({\mathcal F},\mu)\). It is shown that if \(f\in L_ 1\) then \(\lim_{t\to 0^+}(1/t)\int^{t}_{0}T_ sf ds\) exists a.e. on X.
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strongly continuous semi group of linear contractions
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