Related papers: Some Remarks on Capacitary Integrals and Measure T…
We establish the Subgradient Theorem for monotone correspondences -- a monotone correspondence is equal to the subdifferential of a potential if and only if it is conservative, i.e. its integral along a closed path vanishes irrespective of…
We explore the interaction between Lebesgue measure and dominating functions. We show, via both a priority construction and a forcing construction, that there is a function of incomplete degree that dominates almost all degrees. This…
The structures $\langle M,\subseteq^M\rangle$ arising as the inclusion relation of a countable model of sufficient set theory $\langle M,\in^M\rangle$, whether well-founded or not, are all isomorphic. These structures $\langle…
This paper considers functional central limit theorems for stationary absolutely regular mixing processes. Bounds for the entropy with bracketing are derived using recent results in Nickl and P\"otscher (2007). More specifically, their…
We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we…
In this paper we introduce a notion of tightness for a family of nonlinear expectations and show that the tightness can be applied to obtain weak compactness in a framework of nonlinear expectation space. This criterion is very useful for…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
The set $M$ of $d\times d$ Hermitian matrices (observables) is studied as a partially ordered set with the L\"{o}wner partial order. Upper and lower sets in it, define the concept of cumulativeness (used mainly with scalar quantities) in…
A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz…
We consider the pointwise approximation of a subharmonic function by the logarithm of the modulus of an entire function up to a bounded quantity. In the case of finite order an estimate from below of the planar Lebesgue measure of an…
The article provides a modest survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract…
In this paper, we prove new existence and multiplicity results for critical points of lower semicontinuous functionals in Banach spaces, complementing the nonsmooth critical point theory set forth by Szulkin and avoiding the need of the…
Capacitary measures form a class of measures that vanish on sets of capacity zero. These measures are compact with respect to so-called $\gamma$-convergence, which relates a sequence of measures to the sequence of solutions of relaxed…
We have calculated the running coupling in SU(2), SU(3), and SU(4) gauge theories to see whether they have infrared fixed points. An infrared fixed point means no confinement: It means that the long-distance physics is conformal, without a…
Lebesgue integration is a well-known mathematical tool, used for instance in probability theory, real analysis, and numerical mathematics. Thus its formalization in a proof assistant is to be designed to fit different goals and projects.…
Entropic uncertainty relations for the position and momentum within the generalized uncertainty principle are examined. Studies of this principle are motivated by the existence of a minimal observable length. Then the position and momentum…
A new notion of typicality for arbitrary probability measures on standard Borel spaces is proposed, which encompasses the classical notions of weak and strong typicality as special cases. Useful lemmas about strong typical sets, including…
We study an integrable Floquet quantum system related to lattice statistical systems in the universality class of dense polymers. These systems are described by a particular non-unitary representation of the Temperley-Lieb algebra. We find…
It is shown that the approximating functions used to define the Bochner integral can be formed using geometrically nice sets, such as balls, from a differentiation basis. Moreover, every appropriate sum of this form will be within a…
We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…