Subsequences and category (Q1970274)
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scientific article; zbMATH DE number 1417969
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Subsequences and category |
scientific article; zbMATH DE number 1417969 |
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Subsequences and category (English)
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19 March 2000
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Main result: Let \((X,\mu)\) be a regular locally compact \(\sigma\)-finite measure space, \(Z\) a separable Banach space, and \(f_n: X\to Z\) a sequence of Borel measurable functions. Suppose that the sequence \(f_n\) diverges \(\mu\)-a.e. Then \(\{s\in S|f_{s_n}\) diverges \(\mu\)-a.e.\} is a residual set in \(S\), where \(S\) stands for the set consisting of all increasing sequences of natural numbers.
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Baire category
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sequence of Borel measurable functions
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