ISSN:0025-584X    

DOI:10.1002/mana.19780810112

出版商:WILEY‐VCH Verlag    

年代:1978

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19780810113

出版商:WILEY‐VCH Verlag    

年代:1978

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19780810114

出版商:WILEY‐VCH Verlag    

年代:1978

数据来源: WILEY

摘要:

AbstractSpecial finite topological decomposition systems were used to get compactifications of topological spaces in [6]. In this paper the notion of finite decomposition systems is applied for topological measure spaces. We get two canonical topological measure spacesX∞andX∞dbeing projective limits of (discrete) finite decomposition systems for each topological measure spaceX= (X, O, A, P) and each net (Aα) α ϵ I of upward filtering finite σ‐algebras inA.X∞is a compact topological measure space and the idea to construct is the same as used in [6]. The compactifications of [6]are cases of some specialX∞. Further on we obtain that each measurable set of the remainder ofX∞has measure zero with respect to the limit measureP∞(Theorem 1).X∞dis the STONE representation spaceX(\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \cup \limits_{\alpha \in I} A\alpha $\end{document}) of\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \cup \limits_{\alpha \in I} A\alpha $\end{document}Aα, hence a Boolean measure space with regular Borel measure. Some measure theoretical and topological relations betweenX,X(\documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \cup \limits_{\alpha \in I} A\alpha $\end{document}) andx(A)wherex(A)is the Stone representation space ofA, are given in Theorem 2. and 4. As a corollary from Theorem 2. we get a measure theoretical‐topological version to the Theorem of Alexandroff Hausdorff for compactT2measure spacesxwith regular Bore

ISSN:0025-584X    

DOI:10.1002/mana.19780810115

出版商:WILEY‐VCH Verlag    

年代:1978

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19780810116

出版商:WILEY‐VCH Verlag    

年代:1978

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19780810117

出版商:WILEY‐VCH Verlag    

年代:1978

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19780810118

出版商:WILEY‐VCH Verlag    

年代:1978

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19780810119

出版商:WILEY‐VCH Verlag    

年代:1978

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19780810120

出版商:WILEY‐VCH Verlag    

年代:1978

数据来源: WILEY

ISSN:0025-584X    

DOI:10.1002/mana.19780810101

出版商:WILEY‐VCH Verlag    

年代:1978

数据来源: WILEY