Symmetric Functions, Lebesgue Measurability, and the Baire Property
نویسندگان
چکیده
منابع مشابه
Ramsey, Lebesgue, and Marczewski Sets and the Baire Property
We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented. Theorem. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets. Theorem. In the Ellentuck topology on [ω] , (s)0 is a proper subset of the...
متن کاملOn the Lebesgue Measurability of Continuous Functions in Constructive Analysis
The paper opens with a discussion of the distinction between the classical and the constructive notions of "computable function." There then follows a description of the three main varieties of modern constructive mathematics: Bishop's constructive mathematics, the recursive constructive mathematics of the Russian School, and Brouwer's intuitionistic mathematics. The main purpose of the paper i...
متن کاملLebesgue Measurability of Separately Continuous Functions and Separability
A connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y , separately continuous function f : X ×Y →R and open set I ⊆R, the set f −1(I) is an Fσ-set) is studied. We show that every completely regular Baire space with the L-property and the countable chain condition is separable and c...
متن کاملWeak difference property of functions with the Baire property
We prove that the class of functions with the Baire property has the weak difference property in category sense. That is, every function for which f(x+h)−f(x) has the Baire property for every h ∈ R can be written in the form f = g+H+φ where g has the Baire property, H is additive, and for every h ∈ R we have φ(x+h)−φ(x) 6= 0 only on a meager set. We also discuss the weak difference property of ...
متن کاملStationary Reflection and the Universal Baire Property
In this note we show that ω1-Universally Baire selfjustifying systems are fully Universally Baire under the Weak Stationary Reflection Principle for Pairs. This involves analyzing the notion of a weakly captured set of reals, a weakening of the Universal Baire property.
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: Proceedings of the American Mathematical Society
سال: 1993
ISSN: 0002-9939
DOI: 10.2307/2160071