Strict topology and perfect measures
نویسندگان
چکیده
منابع مشابه
The Strict Topology and Compactness in the Space of Measures
The strict topology j3 on the space C(S) of bounded complex valued continuous functions on a locally compact space 5 was introduced by R. C. Buck [ l ] and has been studied by Glicksberg [4] and Wells [9], Among the problems in mathematics which have seen successful applications of the strict topology are various ones in spectral synthesis (Herz [6]) and spaces of bounded analytic functions (Sh...
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Let fibea nonzero positive perfect measure on a o-algebra of subsets of a set X. It is proved that if [A¡: i e /} is a partition of X with p*(A¡) = 0 for all i & I and the cardinal of / non-(Ulam-) measurable, then there is J c / such that U ,<=y A¡ is not ¿i-measurable, generalizing a theorem of Solovay about the Lebesgue measure. This result is used for the study of perfect measures on topolo...
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An interesting example of a compact Hausdorff space that is often presented in beginning courses in topology is the unit square [0, 1]× [0, 1] with the lexicographic order topology. The closed subspace consisting of the top and bottom edges is perfectly normal. This subspace is often called the Alexandroff double arrow space. It is also sometimes called the “split interval”, since it can be obt...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1990
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1990.102354