منابع مشابه
On the Continuity of Haar Measure on Topological Groupoids
It is shown that continuity of a family of invariant (Haar) measures on a topological groupoid G is equivalent to the continuity of the implied convolution product f * g for all pairs of functions / and g. An example is given of a groupoid which admits no (continuous) Haar measure. It results, therefore, that the usual C*-algebra associated with a Haar measure on G cannot, in general, be constr...
متن کاملThe Haar Measure
In this section, we give a brief review of the measure theory which will be used in later sections. We use [R, Chapters 1 and 2] as our main resource. A σ-algebra on a set X is a collectionM of subsets of X such that ∅ ∈M, if S ∈M, then X \ S ∈ M, and if a countable collection S1, S2, . . . ∈ M, then ∪i=1Si ∈ M. That is, M is closed under complements and countable unions, and contains the empty...
متن کاملA Property of the Haar Measure of Some Special LCA Groups
The Euclidean group (Rn,+) where (n?N, plays a key role in harmonic analysis. If we consider the Lebesgue measure ()nd?xR as the Haar measure of this group then 12(2)()nd?x=d?RR. In this article we look for LCA groups K, whose Haar measures have a similar property. In fact we will show that for some LCA groups K with the Haar measure K?, there exists a constant such that 0KC>()(2)KKK?A=C?A for ...
متن کاملA SHORT PROOF FOR THE EXISTENCE OF HAAR MEASURE ON COMMUTATIVE HYPERGROUPS
In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.
متن کاملA Generalization of Bounded Haar Measure.
We wish to thank Karen Rutherford, Erna Rollefson, Charles Hill, and Douglas MacPherson for assistance in various phases of these experiments, and Julius Adler for the Lederberg mutants and helpful comments. The following abbreviations are used: Gal, galactose; Gal-1-P, a-D-galactose-1-phosphate; G-1-P, a-D-glucose-l-phosphate; G-6-P, glucose-6-phosphate; UDPGal, uridine diphosphogalactose; UDP...
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ژورنال
عنوان ژورنال: Comptes Rendus. Mathématique
سال: 2021
ISSN: 1778-3569
DOI: 10.5802/crmath.183