On the spectral SLLN and pointwise ergodic theorem in \(L^{\alpha}\) (Q1203654)
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scientific article; zbMATH DE number 120261
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the spectral SLLN and pointwise ergodic theorem in \(L^{\alpha}\) |
scientific article; zbMATH DE number 120261 |
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On the spectral SLLN and pointwise ergodic theorem in \(L^{\alpha}\) (English)
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22 February 1993
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The harmonic representation of a process with respect to a bounded in some sense random measure is essentially employed for obtaining criteria for SLLN to hold as well as in the case of some classes of operators between \(L^ \alpha\)-spaces, \(1\leq\alpha<\infty\), for the pointwise ergodic theorem to hold. As corollaries some special processes are discussed and iff-conditions presented. Some extensions of the SLLN to random fields are also considered.
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strong law of large numbers
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harmonic representation
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pointwise ergodic theorem
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