3 Notes on Metrics , Measures , and Dimensions Stephen Semmes

3 Notes on Metrics , Measures , and Dimensions Stephen Semmes Department of Mathematics Rice University

Preface In this monograph various notions related to metric spaces are considered, including Hausdorff-type measures and dimensions, Lipschitz mappings, and the Hausdorff distance between nonempty closed and bounded subsets of a metric space. Some familiarity with basic topics in analysis such as Riemann integrals, open and closed sets, and continuous functions is assumed, as in [50, 88, 160], ...

3 Notes on Metrics , Measures , and Dimensions

Preface In this monograph various notions related to metric spaces are considered, including Hausdorff-type measures and dimensions, Lipschitz mappings, and the Hausdorff distance between nonempty closed and bounded subsets of a metric space. Some familiarity with basic topics in analysis such as Riemann integrals, open and closed sets, and continuous functions is assumed, as in [60, 100, 187],...

Notes on Metrics, Measures, and Dimensions

Preface In this monograph various notions of measure and content for subsets of metric spaces are considered, and both metric and topological notions of dimension. Some familiarity with basic topics in analysis such as Riemann integrals, metric spaces, and continuous functions is assumed, as in [50, 88, 160], for instance, although a number of definitions and results that are needed are reviewe...

Some notes on harmonic and holomorphic functions

These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, where “holomorphic” refers to ordinary complex analysis in dimension 2 and generalizations using quaternions and Clifford algebras in higher dimensions. Among the principal themes are weak solutions, the mean-value property, and subharmonicity.

Notes on commutative algebra and harmonic analysis