13 citations · 46 across the 16 of their papers we have counts for
5 papers · 1 filter
Zero Harmonic Density implies Zero Density
Rafael Reno S. Cantuba
A set of integers has zero harmonic density if its elements, viewed as frequencies of continuous characters of the unit circle as a compact group, are measure-theoretically sparse…
Extension Theorems in Measure and Integration Theory as Completeness Axioms
Rafael Reno S. Cantuba
In measure and integration theory, the themes of extending premeasures to outer measures and extending Daniell linear functionals to Daniell integrals are governed by the foundatio…
Sufficient Conditions for Strong Natural Boundaries involving Lacunary Sequences
Rafael Reno S. Cantuba
The notion of a regular point is extended to that of a weak regular point, and so the notion of a strong natural boundary may be described locally as the absence of weak regular po…
A Kronecker-Weyl Theorem from Interpolation Sets
Rafael Reno S. Cantuba
An analog of the classical Kronecker-Weyl theorem for weak uniform distribution is obtained for an arbitrary countably infinite independent subset of a discrete abelian group using…
Five Circles: Real Analysis Theorems equivalent to Completeness
Rafael Cantuba
This is an exposition of the work of O. Riemenschneider about five ''circles'' of implications relating real analysis theorems each equivalent to the Dedekind completeness of the r…