Pseudo-D-lattices and separating points of measures
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- 作者：Anna Avallone <sup>anna.avallone@unibas.it" class="auth_mail" title="E-mail the corresponding authorsup> ; Paolo Vitolo<sup> ; sup><sup>paolo.vitolo@unibas.it" class="auth_mail" title="E-mail the corresponding authorsup>
- 关键词：Mathematics ; Analysis ; Measure theory
- 刊名：Fuzzy Sets and Systems
- 出版年：2016
- 出版时间：15 April 2016
- 年：2016
- 卷：289
- 期：Complete
- 页码：43-63
- 全文大小：435 K
文摘
In 1986, A. Basile and H. Weber proved that every countable family M of σ-additive measures on a σ-complete Boolean ring R admits a dense <span id="mmlsi1" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0165011415003048&_mathId=si1.gif&_user=111111111&_pii=S0165011415003048&_rdoc=1&_issn=01650114&md5=afd8952eb05a86bb366881fc362dde60" title="Click to view the MathML source">G<sub>δsub>span><span class="mathContainer hidden"><span class="mathCode">span>span>span>-set of separating points, with respect to a suitable topology, in the following two cases: either (i) each element of M is s-bounded and, whenever <span id="mmlsi2" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0165011415003048&_mathId=si2.gif&_user=111111111&_pii=S0165011415003048&_rdoc=1&_issn=01650114&md5=cb2ca3c13e56605bee7edc30a020de1d" title="Click to view the MathML source">λ,ν∈Mspan><span class="mathContainer hidden"><span class="mathCode">span>span>span> are distinct, the quotient of R modulo <span id="mmlsi3" class="mathmlsrc"><span class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0165011415003048&_mathId=si3.gif&_user=111111111&_pii=S0165011415003048&_rdoc=1&_issn=01650114&md5=bcebe8ca5ad503486c5d94b9bcf3e8ab" title="Click to view the MathML source">N(λ−ν)span><span class="mathContainer hidden"><span class="mathCode">span>span>span> is infinite, or (ii) each element of M is continuous. In this paper we consider modular measures on lattice-ordered pseudo-effect algebras. Using topological methods, we extend the result of Basile and Weber in a way that allows to unify the above two cases (i) and (ii). This gives a new contribution also in the classical setting of algebras of sets.