Related papers: Notes on metrics, measures, and dimensions

Basic properties of Hausdorff content, dimension, and measure of subsets of metric spaces are discussed, especially in connection with Lipschitz mappings and topological dimension.

These informal notes briefly discuss some basic topics involving Lipschitz functions, connectedness, and Hausdorff content in particular.

These are some basic notes concerning Holder and Lipschitz classes on metric spaces.

These notes, associated with a topics course, are concerned with Hausdorff measures and Lipschitz functions on metric spaces.

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

In this short note, we show that, in any given metric space, every Lipschitz open-map image of every subset of a given metric space whose boundary is Hausdorff-null is Hausdorff-measurable with respect to the same dimension. The main…

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.

The standard arithmetic measures of center, the mean and median, have natural topological counterparts which have been widely used in continuum theory. In the context of metric spaces it is natural to consider the Lipschitz continuous…

These notes, associated with a topics course, are largely concerned with Hausdorff measures and a class of metric spaces which behave like Cantor sets.

Here Lipschitz conditions are used as a primary tool, for studying curves in metric spaces in particular.

The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…

These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.

Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…

These informal notes deal with some topics related to analysis on metric spaces.

This short note describes a connection between algorithmic dimensions of individual points and classical pointwise dimensions of measures.

A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first…

This note is motivated by recent studies by Eriksson-Bique and Soultanis about the construction of charts in general metric measure spaces. We analyze their construction and provide an alternative and simpler proof of the fact that these…