Borel and continuous systems of measures
نویسندگان
چکیده
منابع مشابه
Loeb 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...
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بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
15 صفحه اولContinuous vs. Borel Reductions
We present some natural examples of countable Borel equivalence relations E, F with E ≤B F such that there does not exist a continuous reduction from E to F .
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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...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2014
ISSN: 0035-7596
DOI: 10.1216/rmj-2014-44-4-1073