Condition \(\Sigma _ 1\) in some generalized Saks spaces (Q1089576)
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scientific article; zbMATH DE number 4004921
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Condition \(\Sigma _ 1\) in some generalized Saks spaces |
scientific article; zbMATH DE number 4004921 |
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Condition \(\Sigma _ 1\) in some generalized Saks spaces (English)
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1986
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In order to built up a general theory of generalized Saks spaces it is advisable to investigate concrete examples of Saks spaces which may be applied in various problems of mathematical analysis. On the base of measures (atomic as well as non-atomic) there are defined some examples of generalized Saks spaces \(X_ S=<\{x\in X:\rho (x)\leq 1\},\rho '>\) where X is a vector space (real or complex) and \(\rho\) and \(\rho\) ' are two modulars. The main results state that \(X_ S\) fulfills the \(\Sigma_ 1\)-condition.
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generalized Saks spaces
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