Metric separability and outer integrals

Metric Properties of Outer Space

We define metrics on Culler-Vogtmann space, which are an analogue of the Teichmüller metric and are constructed using stretching factors. In fact the metrics we study are related, one being a symmetrised version of the other. We investigate the basic properties of these metrics, showing the advantages and pathologies of both choices. We show how to compute stretching factors between marked metr...

Non-absolutely Convergent Integrals in Metric Spaces

Concerning the Separability of Certain Locally Connected Metric Spaces

If a connected metric space S is locally separable, then S is separable. If a connected, locally connected, metric space S is locally peripherally separable, then S is separable. Furthermore if a connected, locally connected, complete metric space S satisfies certain "flatness" conditions, it is known to be separable. These "flatness" conditions are rather strong and involve both im kleinen and...

Fractional type Marcinkiewicz integrals over non-homogeneous metric measure spaces

*Correspondence: [email protected] College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China Abstract The main goal of the paper is to establish the boundedness of the fractional type Marcinkiewicz integralMβ ,ρ ,q on non-homogeneous metric measure space which includes the upper doubling and the geometrically doubling conditions. Under the a...

Sampling algorithms of pure network topologies: Stability and separability of metric embeddings

In a time of information glut, observations about complex systems and phenomena of interest are available in several applications areas, such as biology and text. As a consequence, scientists have started searching for patterns that involve interactions among the objects of analysis, to the effect that research on models and algorithms for network analysis has become a central theme for KDD. Th...