Related papers: A study of measure-theoretic area formulas
We calculate a projective space of essential measured laminations in a surface pair, which will be used in another paper to help describe spaces of "finite height laminations."
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
I survey problems concerning Lindelof spaces which have partial set- theoretic solutions.
In this article, the author proposes another way to define the completion of a metric space, which is different from the classical one via the dense property, and prove the equivalence between two definitions. This definition is based on…
This manuscript extends the Cantor-Kuratowski intersection theorem from the setting of metric spaces to the setting of uniformizable spaces. Complete uniformizable spaces are revisited.
In this paper, ideas of open ball, closed ball, compact set are introduced and some related basic properties are studied. Some topological properties and some other well known results of metric spaces including Cantor intersection theorem…
We study tetrahedra and the space of tetrahedra from the viewpoint of local and global maxima for intrinsic distance functions.
Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…
We develop a theory of `non-uniformly local' tent spaces on metric measure spaces. As our main result, we give a remarkably simple proof of the atomic decomposition.
We study the phase space of the equations of Ince's table from the viewpoint of its accessible singularities and local index.
The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…
Measure structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure structured deformation is defined via relaxation departing either from energies associated with…
We obtain an explicit formula for comparing total curvature of level sets of functions on Riemannian manifolds, and develop some applications of this result to the isoperimetric problem in spaces of nonpositive curvature.
We investigate extension of a measure to a very general set of undetermined structure. Structure may be imposed on this set in special cases
We characterize all the phase space measurements for a non-relativistic particle.
Bell tests are of profound statistical nature. Besides physical considerations, the proper understanding of their implications should involve detailed statistical analyses. In this regard, recent works have shown that their consequences and…
We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We illustrate, through examples, how the deterministic and…
We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we…
In this paper, using a more generalized inequality instead of triangle inequality, the notion of \theta-metric space is introduced. Some important properties of induced topology by such spaces are presented. Also, Banach and Caristi type…
We provide an introduction to mathematical theory of scattering resonances and survey some recent results.