Related papers: A beginner's guide to analysis on metric spaces

These notes deal with metric spaces, Hausdorff measures and dimensions, Lipschitz mappings, and related topics. The reader is assumed to have some familiarity with basic analysis, which is also reviewed.

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

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

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

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…

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

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

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

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

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…

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

These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.

In this brief survey we give an introduction to some aspects of "atoms" on metric spaces and their connection with linear operators.

This short survey has been prepared in connection with the workshop on discrete metric spaces and their applications at Princeton, August, 2003, and tries to convey some of the ways that one might look at functions on metric spaces in…

These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.

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.

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…

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

The aim of this note is to prove that any compact metric space can be made connected at a minimal cost, where the cost is taken to be the one-dimensional Hausdorff measure.