Related papers: Potpourri, 10

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

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

These notes, associated with a topics course, are concerned with some general methods related to norms and linear transformations.

These notes are connected to a "potpourri" topics class and deal with some basic issues involving norms and convexity.

These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.

These notes, connected to a "potpourri" topics course currently underway, are concerned with some interrelated themes of polynomials, functions on the unit circle or interval, and norms.

These notes, associated with a topics course, deal with some special cases involving norms and linear transformations.

These notes are connected to a "potpourri" topics class and deal with some special cases of norms of various objects which arise in classical analysis.

These notes deal with some topics related to limits of norms, functions on the unit circle, and so on.

These notes, associated with a topics course, deal with some special features of summability and supremum norms which are often useful.

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.

In this paper we study a class of random Cantor sets. We determine their almost sure Hausdorff, packing, box, and Assouad dimensions. From a topological point of view, we also compute their typical dimensions in the sense of Baire category.…

We study a generalization of Mor\'an's sum sets, obtaining information about the $h$-Hausdorff and $h$-packing measures of these sets and certain of their subsets.

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

These informal notes briefly discuss various aspects of Cantor sets.

We establish a formula yielding the Hausdorff measure for a class of non-self-similar Cantor sets in terms of the canonical covers of the Cantor set.

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

In this paper we define a new class of metric spaces, called multi-model Cantor sets. We compute the Hausdorff dimension and show that the Hausdorff measure of a multi-model Cantor set is finite and non-zero. We then show that a bilipschitz…

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

We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure…