Note on support-concentrated Borel measures
نویسندگان
چکیده
منابع مشابه
On Separable Supports of Borel Measures
Some properties of Borel measures with separable supports are considered. In particular, it is proved that any σ-finite Borel measure on a Suslin line has a separable supports and from this fact it is deduced, using the continuum hypothesis, that any Suslin line contains a Luzin subspace with the cardinality of the continuum. Let E be a topological space. We say that the space E has the propert...
متن کاملOn the Extension of Borel Measures
The class of Borel sets in a locally compact space is the cr-ring generated by the compact sets [3, p. 219], while the class of weakly Borel sets is the (r-algebra generated by the closed sets [2]. The object of this note is to show that any measure defined on the class of Borel sets may be extended to the class of weakly Borel sets in a simple and canonical way (Theorem 1). There is a useful a...
متن کاملLoeb Measures and Borel Algebras
It is shown that a measurable function from an atomless Loeb probability space (Ω,A, P ) to a Polish space is at least continuum-to-one valued almost everywhere. It follows that there is no injective mapping h : [0, 1] → Ω such that h([a, b]) is Loeb measurable for each 0 ≤ a < b ≤ 1 and P (h([0, 1])) > 0. Thus, when an atomless Loeb measurable algebra on an internal set of cardinality continuu...
متن کاملInvariant Measures Concentrated on Countable Structures
Let L be a countable language. We say that a countable infinite L-structure M admits an invariant measure when there is a probability measure on the space of L-structures with the same underlying set as M that is invariant under permutations of that set, and that assigns measure one to the isomorphism class of M. We show that M admits an invariant measure if and only if it has trivial definable...
متن کاملOn Typical Markov Operators Acting on Borel Measures
Generic properties of different objects (functions, sets, measures, and many others) have been studied for a long time (see [1, 2, 3, 4, 5, 7, 8, 9, 10, 13, 15, 16]). We say that some property is generic (or typical) if the subset of all elements satisfying this property is residual. Recall that a subset of a complete metric space is residual if its complement can be represented as a countable ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1980
ISSN: 0263-6115
DOI: 10.1017/s1446788700021303