Titlebook: Uniform Spaces and Measures; Jan Pachl Book 2013 Springer Science+Business Media New York 2013 abstract harmonic analysis.semitopological

Commission

Prerequisitesmmarized in this chapter, along with notation conventions. Definitions of common terms and most proofs are omitted. Detailed explanations and proofs may be found in the reference works cited in each section.

RADE

Induced Uniform Structurespaces, one uniformity on . is the coarsest for which the mappings are uniformly continuous. This is the induced uniformity on ., also known as the projectively induced or projectively generated uniformity. Special cases of this construction are the uniform subspace, the uniform and semiuniform produ

摇晃

myopia

Instances of Uniform Measuresow to derive properties of spaces of measures from the results in Chap. 6. Although many of the theorems derived here are well known, it is noteworthy that they are all obtained as special cases of general theorems about uniform measures. This brings out parallels between various spaces of measures

Memorial

Direct Product and Convolutionces and on topological groups. In this chapter I explore the connection between uniform measures and convolution in a fairly general setting that includes convolution on topological groups as a special case.

半球

Free Uniform Measuresn the space of all (not necessarily bounded) uniformly continuous functions. The “unbounded version” of . is the space . of .. The adjective . refers to a universal property of . that characterizes free functors.

faction

Approximation of Probability Distributionsf seminorms ∥ ⋅ ∥. on a large subspace of .. In Sect. 11.2, I discuss properties of asymptotic approximation for nets of probability distributions and apply Corollary P.43 to show that certain notions of approximation are all equivalent on sequences of distributions.

起波澜

Debate

Book 2013cently uniform measures reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered through many papers written by a number of authors, some unpublished, written using a variety of definitions and notations. Uniform measures are certain funct

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