Related papers: A note on Cybenko's Universal Approximation Theore…
We reconsider a well known problem of quantum theory, i.e. the so called measurement (or macro-objectification) problem, and we rederive the fact that it gives rise to serious problems of interpretation. The novelty of our approach derives…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
Recently, it has been stated that single-world interpretations of quantum theory are logically inconsistent. The claim is derived from contradicting statements of agents in a setup combining two Wigner's-friend experiments. Those statements…
Three recent arguments seek to show that the universal applicability of unitary quantum theory is inconsistent with the assumption that a well-conducted measurement always has a definite physical outcome. In this paper I restate and analyze…
Approximation in measure is employed to solve an asymptotic Dirichlet problem on arbitrary open sets and to show that many functions, including the Riemann zeta-function, are universal in measure. Connections with the Riemann Hypothesis are…
In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, g-continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove results on…
In the article "Universal Densities Exist for Every Finite Reference Measure" (IEEE Trans. Inform. Theory, vol. 69, no. 8, pp. 5277--5288, 2023) we neglected to mention relevant contributions of Boris Ryabko. We cited a source by him that…
In this paper we correct an inaccuracy that appears in the proof of Theorem 1. in Czerwik's article "Contraction mappings in $b$-metric spaces.", Acta Math. Inform. Univ. Ostraviensis, 1:5--11, 1993.
We aim to fill a gap in the proof of an inequality relating two exponents of uniform Diophantine approximation stated in a paper by Bugeaud. We succeed to verify the inequality in several instances, in particular for small dimension.…
These series of notes serve as an introduction to some of both the classical and modern techniques in Reifenberg theory. At its heart, Reifenberg theory is about studying general sets or measures which can be, in one sense or another,…
Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the…
The notion of measurements is central for many debates in quantum mechanics. One critical point is whether a measurement can be regarded as an absolute event, giving the same result for any observer in an irreversible manner. Using ideas…
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement and the resultant observation (observer) effect of statistical nature. Owing to its simplicity and operational tangibility, our general…
A complete theory of overmeasurement by measuring refinements of observables is presented. It encompasses a wider set of functions of observ- ables (coarsenings) . Thus the theory has a broad potential application.It is applied to a…
We develop a Glivenko--Cantelli theory for monotone, almost additive functions of i.\,i.\,d.\ sequences of random variables indexed by~$\Z^d$. Under certain conditions on the random sequence, short range correlations are allowed as well. We…
The term Gibbons conjecture is widely used in connection with symmetry results for the Allen-Cahn equation. However, its origin is less transparent than its frequent citation suggests. In this note, we revisit its emergence, tracing it to a…
In a recent article, Khrennikov claims that a particular theorem about agreement between quantum measurement results poses a problem for the interpretation of quantum mechanics known as QBism. Considering the basic setup of that theorem in…
In recent years, novel quantifications of measurement error in quantum mechanics have for the first time enabled precise formulations of Heisenberg's famous but often challenged measurement uncertainty relation. These relations take the…
A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…
This short note gives an elementary alternative proof for a theorem of Danilov and Koshevoy on Minkowski summation and unimodularity in discrete convex analysis. It is intended to disseminate this fundamental theorem and make its proof…