Baire Category Lower Density Operators with Borel Values
نویسندگان
چکیده
Abstract We prove that the lower density operator associated with Baire category points in real line has Borel values of class $$\pmb \Pi ^0_3$$ Π 3 0 which is analogous to measure case. also introduce notion point a subset property Cantor space, and we it generates .
منابع مشابه
Covering with universally Baire operators∗†
We introduce a covering conjecture and show that it holds below ADR + “Θ is regular”. We then use it to show that in the presence of mild large cardinal axioms, PFA implies that there is a transitive model containing the reals and ordinals and satisfying ADR + “Θ is regular”. The method used to prove the Main Theorem of this paper is the core model induction. The paper contains the first applic...
متن کاملFinite Generators for Countable Group Actions in the Borel and Baire Category Settings
For a continuous action of a countable discrete group G on a Polish space X, a countable Borel partition P of X is called a generator if GP ∶= {gP ∶ g ∈ G,P ∈ P} generates the Borel σ-algebra of X. For G = Z, the Kolmogorov–Sinai theorem gives a measuretheoretic obstruction to the existence of finite generators: they do not exist in the presence of an invariant probability measure with infinite...
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 کاملBorel Extensions of Baire Measures in Zfc
We prove: (1) Every Baire measure on the Kojman-Shelah Dowker space [10] admits a Borel extension. (2) If the continuum is not a real-valued measurable cardinal then every Baire measure on the M. E. Rudin Dowker space [16] admits a Borel extension. Consequently, Balogh’s space [3] remains as the only candidate to be a ZFC counterexample to the measure extension problem of the three presently kn...
متن کاملBaire reductions and good Borel reducibilities
In [8] we have considered a wide class of “well-behaved” reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degree-structures induced by good Borel reducibilities. This extends and improves the results of [8] allowing to deal with a larger class of notions of reduction (including, among others, the Baire clas...
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: Results in Mathematics
سال: 2022
ISSN: ['1420-9012', '1422-6383']
DOI: https://doi.org/10.1007/s00025-022-01781-7