A Course on Borel Sets
نویسنده
چکیده
منابع مشابه
Notes on Sigma Algebras for Brownian Motion Course
The space R comes with its standard topology which we denote byO (that is, O is the collection of open sets in R). It comes also with its Borel sigma algebra which we denote by B. The Borel sigma algebra is the smallest one containing all open sets (i.e., the sigma algebra generated by O). Let I be an arbitrary non-empty set (finite, countable or uncountable). For x ∈ I, the coordinate function...
متن کاملMeasure Theory , 2007
I will assume familiarity with the basic measure from chapters 12 and 13 of [5], though a brief summary is given below. [7] provides an excellent general reference for measure theory and analysis. Later in the course we will explore topics in ergodic theory, and here one could refer to [6]. As we push on I will attempt to update the references. These notes are a work in progress. Let me know ab...
متن کاملOn Borel Mappings and Σ-ideals Generated by Closed Sets
We obtain some results about Borel maps with meager fibers on completely metrizable separable spaces. The results are related to a recent dichotomy by Sabok and Zapletal, concerning Borel maps and σ-ideals generated by closed sets. In particular, we give a “classical” proof of this dichotomy. We shall also show that for certain natural σ-ideals I generated by closed sets in compact metrizable s...
متن کاملCanonizing relations on nonsmooth sets
We show that any symmetric, Baire measurable function from the complement of E0 to a finite set is constant on an E0-nonsmooth square. A simultaneous generalization of Galvin’s theorem that Baire measurable colorings admit perfect homogeneous sets and the Kanovei-Zapletal theorem canonizing Borel equivalence relations on E0-nonsmooth sets, this result is proved by relating E0-nonsmooth sets to ...
متن کاملPotential Wadge classes
Let Γ be a Borel class, or a Wadge class of Borel sets, and 2≤d≤ω a cardinal. We study the Borel subsets of R that can be made Γ by refining the Polish topology on the real line. These sets are called potentially Γ. We give a test to recognize potentially Γ sets. 2010 Mathematics Subject Classification. Primary: 03E15, Secondary: 54H05, 28A05, 26A21
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره 180 شماره
صفحات -
تاریخ انتشار 2008