The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Characterizations of p-superharmonic functions on metric spaces”

The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces

Marcello Lucia, Michael J. Puls (2015)

Analysis and Geometry in Metric Spaces

Similarity:

Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfies certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.

Spaces of σ-finite linear measure

Ihor Stasyuk, Edward D. Tymchatyn (2013)

Colloquium Mathematicae

Similarity:

Spaces of finite n-dimensional Hausdorff measure are an important generalization of n-dimensional polyhedra. Continua of finite linear measure (also called continua of finite length) were first characterized by Eilenberg in 1938. It is well-known that the property of having finite linear measure is not preserved under finite unions of closed sets. Mauldin proved that if X is a compact metric space which is the union of finitely many closed sets each of which admits a σ-finite linear...

A note on global integrability of upper gradients of p-superharmonic functions

Outi Elina Maasalo, Anna Zatorska-Goldstein (2009)

Colloquium Mathematicae

Similarity:

We consider a complete metric space equipped with a doubling measure and a weak Poincaré inequality. We prove that for all p-superharmonic functions there exists an upper gradient that is integrable on H-chain sets with a positive exponent.

Fubini’s Theorem on Measure

Noboru Endou (2017)

Formalized Mathematics

Similarity:

The purpose of this article is to show Fubini’s theorem on measure [16], [4], [7], [15], [18]. Some theorems have the possibility of slight generalization, but we have priority to avoid the complexity of the description. First of all, for the product measure constructed in [14], we show some theorems. Then we introduce the section which plays an important role in Fubini’s theorem, and prove the relevant proposition. Finally we show Fubini’s theorem on measure.

Product Pre-Measure

Noboru Endou (2016)

Formalized Mathematics

Similarity:

In this article we formalize in Mizar [5] product pre-measure on product sets of measurable sets. Although there are some approaches to construct product measure [22], [6], [9], [21], [25], we start it from σ-measure because existence of σ-measure on any semialgebras has been proved in [15]. In this approach, we use some theorems for integrals.

John-Nirenberg lemmas for a doubling measure

Daniel Aalto, Lauri Berkovits, Outi Elina Kansanen, Hong Yue (2011)

Studia Mathematica

Similarity:

We study, in the context of doubling metric measure spaces, a class of BMO type functions defined by John and Nirenberg. In particular, we present a new version of the Calderón-Zygmund decomposition in metric spaces and use it to prove the corresponding John-Nirenberg inequality.

Construction of Measure from Semialgebra of Sets1

Noboru Endou (2015)

Formalized Mathematics

Similarity:

In our previous article [22], we showed complete additivity as a condition for extension of a measure. However, this condition premised the existence of a σ-field and the measure on it. In general, the existence of the measure on σ-field is not obvious. On the other hand, the proof of existence of a measure on a semialgebra is easier than in the case of a σ-field. Therefore, in this article we define a measure (pre-measure) on a semialgebra and extend it to a measure on a σ-field. Furthermore,...