Criteria for σ-Smoothness, τ-Smoothness, and Tightness of Lattice Regular Measures, with Applications
| Autor: | Panagiotis D. Stratigos, George Bachman |
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| Rok vydání: | 1981 |
| Předmět: | |
| Zdroj: | Canadian Journal of Mathematics. 33:1498-1525 |
| ISSN: | 1496-4279 0008-414X |
| Popis: | Consider an arbitrary set X and an arbitrary disjunctive lattice of subsets of X, ℒ. The algebra of subsets of X generated by ℒ is denoted by , the set of all ℒ-regular measures on , by MR(ℒ), and the associated Wallman space, a compact T1 space, by IR(ℒ); assume X is embedded in IR(ℒ) (otherwise, consider the image of X in IR(ℒ)).In part of an earlier paper [4] the work of Knowles [15] and Gould and Mahowald [11] was generalized from the explicit topological setting of X, a Tychonoff space, with ℒ the lattice of zero sets of X, to the above setting, with the added assumption that ℒ was also δ and normal. This was done so that the important Alexandroff Representation Theorem [1] could be utilized in order to induce two associated measures , and defined on and respectively, where W(ℒ) is the Wallman lattice in IR(ℒ). |
| Databáze: | OpenAIRE |
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