Towers of Borel Functions
نویسنده
چکیده
We give mathematical reformulations of the cardinals p and t in terms of families of Borel functions. As an application we show that t is invariant under the addition of a single Cohen real.
منابع مشابه
Five-value rich lines, Borel directions and uniqueness of meromorphic functions
For a meromorphic function $f$ in the complex plane, we shall introduce the definition of five-value rich line of $f$, and study the uniqueness of meromorphic functions of finite order in an angular domain by involving the five-value rich line and Borel directions. Finally, the relationship between a five-value rich line and a Borel direction is discussed, that is, every Borel direction of $f$ ...
متن کاملA Borel-cantelli Lemma for Nonuniformly Expanding Dynamical Systems
Let (An)n=1 be a sequence of sets in a probability space (X,B, μ) such that P∞ n=1 μ(An) =∞. The classical Borel-Cantelli lemma states that if the sets An are independent, then μ({x ∈ X : x ∈ An for infinitely many values of n}) = 1. We present analogous dynamical Borel-Cantelli lemmas for certain sequences of sets (An) inX (including nested balls) for a class of deterministic dynamical systems...
متن کاملGeneralizations of Borel-Cantelli Lemma
The Borel-Cantelli Lemma is very important in the probability theory. In this paper, we first describe the general case of the Borel-Cantelli Lemma. The first part of this lemma, assuming convergence and the second part includes divergence and independence assumptions. In the following, we have brought generalizations of the first and second part of this lemma. In most generalizat...
متن کاملWhen are Borel functions Baire functions ?
The following two theorems give the flavour of what will be proved. THEOREM. Let Y be a complete metric space. Then the families of first Baire class functions and of first Borel class functions from [0, 1] to Y coincide if and only if Y is connected and locally connected. THEOREM. Let Y be a separable metric space. Then the families of second Baire class functions and of second Borel class fun...
متن کاملEffective Borel measurability and reducibility of functions
The investigation of computational properties of discontinuous functions is an important concern in computable analysis. One method to deal with this subject is to consider effective variants of Borel measurable functions. We introduce such a notion of Borel computability for single-valued as well as for multi-valued functions by a direct effectivization of the classical definition. On Baire sp...
متن کامل