منابع مشابه
Cross Sections of Borel Flows with Restrictions on the Distance Set
Given a set of positive reals, we provide a necessary and sufficient condition for a free Borel flow to admit a cross section with all distances between adjacent points coming from this set.
متن کاملSolids Whose Parallel Cross-Sections are Regular Polygons
Given a solid in R3 whose base is contained in the xy-plane and parallel cross-sections perpendicular to the xy-plane are regular polygons, the volume and surface area are determined. Additionally, the asymptotic behavior of the solid as the number of sides of the crosssectional polygon increases is analyzed.
متن کاملCross Sections for Geodesic Flows and Α-continued Fractions
We adjust Arnoux’s coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the α-continued fractions, for each α ∈ (0, 1]. The argument applies in wide generality, as we illustrate with its application to the Rosen continued fractions and their recently introduced ...
متن کاملAn Uncountable Family of Regular Borel measures
3 ABSTRACT. Let c > 0 be a fixed constant. Let 0 ≤ r < s be an arbitrary pair of real numbers. Let a, b be any pair of real numbers such that | b − a | ≤ c(s − r). Define C s r to be the set of continuous real-valued functions on [r, s], and define C r to be the set of continuous real-valued functions on [ r, +∞). Finally, consider the following sets of Lipschitz functions:
متن کاملBorel Classes of Uniformizations of Sets with Large Sections
We give several refinements of known theorems on Borel uniformizations of sets with ”large sections”. In particular, we show that a set B ⊂ [0, 1] × [0, 1] which belongs to Σ0α, α ≥ 2, and which has all ”vertical” sections of positive Lebesgue measure, has a Π0α uniformization which is the graph of a Σ0α-measurable mapping. We get a similar result for sets with nonmeager sections. As a corollar...
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: Journal of the European Mathematical Society
سال: 2019
ISSN: 1435-9855
DOI: 10.4171/jems/879