Results 1 to 10 of about 73 (71)
On Banach and Kuratowski Theorem, K-Lusin sets and strong sequences
Open Mathematics, 2018 In 2003 Bartoszyński and Halbeisen published the results on various equivalences of Kuratowski and Banach theorem from 1929 concerning some aspect of measure theory.
Jureczko Joanna
doaj +2 more sources
Normal bundle and Almgren’s geometric inequality for singular varieties of bounded mean curvature [PDF]
Bulletin of Mathematical Sciences, 2020 In this paper we deal with a class of varieties of bounded mean curvature in the viscosity sense that has the remarkable property to contain the blow up sets of all sequences of varifolds whose mean curvatures are uniformly bounded and whose boundaries ...
Mario Santilli
doaj +1 more source
On the double Lusin condition and convergence theorem for Kurzweil-Henstock type integrals [PDF]
Mathematica Bohemica, 2016 Equiintegrability in a compact interval $E$ may be defined as a uniform integrability property that involves both the integrand $f_n$ and the corresponding primitive $F_n$.
Abraham Racca, Emmanuel Cabral
doaj +1 more source
On a geometric combination of functions related to Prékopa–Leindler inequality
Mathematika, Volume 69, Issue 2, Page 482-507, April 2023., 2023 Abstract We introduce a new operation between nonnegative integrable functions on Rn$\mathbb {R}^n$, that we call geometric combination; it is obtained via a mass transportation approach, playing with inverse distribution functions. The main feature of this operation is that the Lebesgue integral of the geometric combination equals the geometric mean ...
Graziano Crasta, Ilaria Fragalà
wiley +1 more source
Journal of Function Spaces, Volume 2023, Issue 1, 2023., 2023 Let L = −Δ + V be a Schrödinger operator on ℝn, where Δ denotes the Laplace operator ∑i=1n∂2/∂xi2 and V is a nonnegative potential belonging to a certain reverse Hölder class RHq(ℝn) with q > n/2. In this paper, by the regularity estimate of the fractional heat kernel related with L, we establish the quantitative weighted boundedness of Littlewood ...
Li Yang, Pengtao Li, Andrea Scapellato
wiley +1 more source
Two‐dimensional metric spheres from gluing hemispheres
Journal of the London Mathematical Society, Volume 106, Issue 4, Page 3069-3102, December 2022., 2022 Abstract We study metric spheres (Z,dZ)$(Z, d_{Z} )$ obtained by gluing two hemispheres of S2$\mathbb {S}^{2}$ along an orientation‐preserving homeomorphism g:S1→S1$g \colon \mathbb {S}^{1} \rightarrow \mathbb {S}^{1}$, where dZ$d_{Z}$ is the canonical distance that is locally isometric to S2$\mathbb {S}^{2}$ off the seam. We show that if (Z,dZ)$(Z, d_{
Toni Ikonen
wiley +1 more source
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 Let (X, d, μ) be a metric measure space endowed with a metric d and a non‐negative Borel doubling measure μ. Let L be a non‐negative self‐adjoint operator on L2(X). Assume that the (heat) kernel associated to the semigroup e−tL satisfies a Gaussian upper bound.
Jiawei Shen +3 more
wiley +1 more source
Lusin-type Theorems for Cheeger Derivatives on Metric Measure Spaces
Analysis and Geometry in Metric Spaces, 2015 A theorem of Lusin states that every Borel function onRis equal almost everywhere to the derivative of a continuous function. This result was later generalized to Rn in works of Alberti and Moonens-Pfeffer.
Guy C. David
doaj +1 more source
The Lusin Theorem and Horizontal Graphs in the Heisenberg Group
Analysis and Geometry in Metric Spaces, 2013 In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz ...
Hajłasz Piotr, Mirra Jacob
doaj +1 more source
Haar null and Haar meager sets: a survey and new results
Bulletin of the London Mathematical Society, Volume 52, Issue 4, Page 561-619, August 2020., 2020 Abstract We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the techniques that may enable the reader to prove results in this area.
Márton Elekes, Donát Nagy
wiley +1 more source