Related papers: A Unified Convergence Theorem
A formalism is presented to construct a non-perturbative Grand Unified Theory when gravitational Planck-scale phenomena are included. The fundamental object on the Planck scale is the three-torus T^3 from which the known properties of…
In the paper, we generalize the Arzel\`a-Ascoli theorem in the setting of uniform spaces. At first, we recall well-known facts and theorems coming from monographs of Kelley and Willard. The main part of the paper introduces the notion of…
We present conditions that allow us to pass from the convergence of probability measures in distribution to the uniform convergence of the associated quantile functions. Under these conditions, one can in particular pass from the asymptotic…
We prove Cuntz-Krieger and graded uniqueness theorems for Steinberg algebras. We also show that a Steinberg algebra is basically simple if and only if its associated groupoid is both effective and minimal. Finally we use results of…
In this note we show that Voevodsky's univalence axiom holds in the model of type theory based on symmetric cubical sets. We will also discuss Swan's construction of the identity type in this variation of cubical sets. This proves that we…
In this paper we study quadratic forms which are universal when restricted to almost prime inputs, establishing finiteness theorems akin to the Conway--Schneeberger 15 theorem.
We prove a generalization of the well known Routh's triangle theorem. As a consequence, we get a unification of the theorems of Ceva and Menelaus. A connection to Feynman's triangle is also given.
The Univalence Principle is the statement that equivalent mathematical structures are indistinguishable. We prove a general version of this principle that applies to all set-based, categorical, and higher-categorical structures defined in a…
We extend the well-known Rainwater-Simons convergence theorem to various generalized convergence methods such as strong matrix summability, statistical convergence and almost convergence. In fact we prove these theorems not only for…
We employ the spectral theory of Eisenstein series to prove that the Hardy sums, integer-valued analogs of the classical Dedekind sums, are uniformly distributed in $\mathbf{Z} / m \mathbf{Z}$ for any integer $m > 1$.
In this paper, we introduce a generalized notion of monotone property and prove some results regarding existence and uniqueness of multi-tupled fixed points for nonlinear contraction mappings satisfying monotone property in ordered complete…
The classical theorem of Birkhoff states that the $T^N f(x) = (1/N)\sum_{k=0}^{N-1} f(\sigma^k x)$ converges almost everywhere for $x\in X$ and $f\in L^{1}(X)$, where $\sigma$ is a measure preserving transformation of a probability measure…
We prove a uniform vector-valued Wiener-Wintner Theorem for a class of operators that includes compositions of ergodic Koopman operators with contractive multiplication operators. Our results are new even in the case of complex-valued…
We prove the internal inconsistency of the supersymmetric Wess-Zumino model. Our proof is based on three assumptions. The first assumption is that in the full theory the structure of counter temcs coincides with the structure of the counter…
The generalization of the Jessen-Marcinkiewicz-Zygmund-type theorem for the abstract space with measure was obtained in current paper. Some applications to classical harmonic analysis were reviewed.
It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p-$space, $1\leq p<\infty$ or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge…
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…
After Voronin proved the universality theorem of the Riemann zeta function in the 1970s, universality theorems have been proposed for various zeta and L-functions. Drungilas-Garunkstis-Kacenas' work at 2013 on the universality theorem of…
This note will present a new proof of the fact that every uniformly bounded group of invertible elements in a finite von Neumann algebra is similar to a unitary group. The proof involves metric geometric arguments in the non-positively…
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…