Measurability of equivalence classes and MEC\(_p\)-property

DOI10.4171/RMI/514zbMath1146.28001OpenAlexW1974348608MaRDI QIDQ925109

Maarit Järvenpää, Sari Rogovin, Nageswari Shanmugalingam, Esa Järvenpää, Kevin Rogovin

Publication date: 29 May 2008

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1204128301

zbMATH Keywords

doubling measurequasi-convexityanalytic set\(p\)-Poincaré inequality\(p\)-integrable upper gradientMEC\(_p\)-space

Mathematics Subject Classification ID

Descriptive set theory (03E15) Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence (28A20) Special maps on metric spaces (54E40) Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) (54H05)

Related Items (19)

Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1-Poincaré inequality ⋮ Some remarks on rectifiably connected metric spaces ⋮ Functions of bounded variation and the \(AM\)-modulus in \(\mathbb{R}^n\) ⋮ On the sharp lower bound for duality of modulus ⋮ Regularity of solutions to the fractional Cheeger-Laplacian on domains in metric spaces of bounded geometry ⋮ An upper gradient approach to weakly differentiable cochains ⋮ Prime ends for domains in metric spaces ⋮ Classification of metric measure spaces and their ends using p-harmonic functions ⋮ Density of Lipschitz functions in energy ⋮ The \(\infty \)-Poincaré inequality on metric measure spaces ⋮ Removable sets for Newtonian Sobolev spaces and a characterization of \(p\)-path almost open sets ⋮ Duality of moduli and quasiconformal mappings in metric spaces ⋮ Relative isoperimetric inequalities and sufficient conditions for finite perimeter on metric spaces ⋮ Quasiopen and \(p\)-path open sets, and characterizations of quasicontinuity ⋮ Comparisons of relative BV-capacities and Sobolev capacity in metric spaces ⋮ \(p\)-hyperbolicity of ends and families of paths in metric spaces ⋮ Local and semilocal Poincaré inequalities on metric spaces ⋮ A new Federer-type characterization of sets of finite perimeter ⋮ Pointwise Lipschitz functions on metric spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Carleson type estimates for \(p\)-harmonic functions and the conformal Martin boundary of John domains in metric measure spaces
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Lectures on analysis on metric spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Ahlfors \(Q\)-regular spaces with arbitrary \(Q>1\) admitting weak Poincaré inequality
• Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings
• Sobolev met Poincaré
• From local to global in quasiconformal structures.
• Harmonic functions on metric spaces

This page was built for publication: Measurability of equivalence classes and MEC\(_p\)-property