Algebras of Measures on a Locally Compact Semigroup II

1970 ◽  
Vol 2 (Part_4) ◽  
pp. 651-659 ◽  
Author(s):  
Anne C. Baker ◽  
J. W. Baker
Keyword(s):  
Compact Semigroup ◽  
Locally Compact ◽  
Locally Compact Semigroup

scholarly journals A note on the idempotent measures on countable semigroups

1970 ◽  
Vol 11 (4) ◽  
pp. 417-420
Author(s):  
Tze-Chien Sun ◽  
N. A. Tserpes
Keyword(s):  
Probability Measure ◽  
Continuous Mapping ◽  
Compact Semigroup ◽  
Probability Measures ◽  
Left Zero ◽  
Product Topology ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Image Position ◽  
Completely Simple

In [6] we announced the following Conjecture: Let S be a locally compact semigroup and let μ be an idempotent regular probability measure on S with support F. Then(a) F is a closed completely simple subsemigroup.(b) F is isomorphic both algebraically and topologically to a paragroup ([2], p.46) X × G × Y where X and Y are locally compact left-zero and right-zero semi-groups respectively and G is a compact group. In X × G × Y the topology is the product topology and the multiplication of any two elements is defined by , x where [y, x′] is continuous mapping from Y × X → G.(c) The induced μ on X × G × Y can be decomposed as a product measure μX × μG× μY where μX and μY are two regular probability measures on X and Y respectively and μG is the normed Haar measure on G.

On the Semigroup of Probability Measures of a Locally Compact Semigroup II

1987 ◽  
Vol 30 (3) ◽  
pp. 273-281 ◽  
Author(s):  
James C. S. Wong
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Compact Semigroup ◽  
Probability Measures ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Fixed Point Properties ◽  
The Relationship ◽  
Locally Compact Semigroups

AbstractThis is a sequel to the author's paper "On the semigroup of probability measures of a locally compact semigroup." We continue to investigate the relationship between amenability of spaces of functions and functionals associated with a locally compact semigroups S and its convolution semigroup MO(S) of probability measures and fixed point properties of actions of S and MO(S) on compact convex sets.

scholarly journals Right invariant integrals on locally compact semigroups

1964 ◽  
Vol 4 (3) ◽  
pp. 273-286 ◽  
Author(s):  
J. H. Michael
Keyword(s):  
Compact Semigroup ◽  
Compact Sets ◽  
Property A ◽  
Locally Compact ◽  
Invariant Integrals ◽  
Positive Linear Functional ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Image Position ◽  
Locally Compact Semigroups

An integral on a locally compact Hausdorff semigroup ς is a non-trivial, positive, linear functional μ on the space of continuous real-valued functions on ς with compact supports. If ς has the property: (A) for each pair of compact sets C, D of S, the set is compact; then, whenever and a ∈ S, the function fa defined by is also in . An integral μ on a locally compact semigroup S with the property (A) is said to be right invariant if for all j ∈ and all a ∈ S.

On r*-Invariant Measure on a Locally Compact Semigroup with Recurrence

1980 ◽  
Vol 23 (2) ◽  
pp. 237-239
Author(s):  
Samuel Bourne
Keyword(s):  
Invariant Measure ◽  
Borel Measure ◽  
Compact Semigroup ◽  
Locally Compact ◽  
Borel Sets ◽  
Left Group ◽  
Locally Compact Semigroup ◽  
Regular Borel Measure

A regular Borel measure μ is said to be r*-invariant on a locally compact semigroup if μ(Ba-1) = μ(B) for all Borel sets B and points a of S, where Ba-1 ={xϵS, xaϵB}. In [1] Argabright conjectured that the support of an r*-invariant measure on a locally compact semigroup is a left group, Mukherjea and Tserpes [4] proved this conjecture in the case that the measure is finite; however their method of proof fails when the measure is infinite.

A non-probabilistic approach to Poisson spaces

1983 ◽  
Vol 93 (3-4) ◽  
pp. 181-188 ◽  
Author(s):  
Alan L. T. Paterson
Keyword(s):  
Probability Theory ◽  
Probability Measure ◽  
Harmonic Functions ◽  
Hausdorff Space ◽  
Probabilistic Approach ◽  
Compact Semigroup ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Poisson Space

SynopsisUsing techniques from probability theory, it has been established that if μ is a probability measure on a separable, locally compact group, then the space of μ-harmonic functions on the group can be identified with C(X) for some compact, Hausdorff space X. The space X is known as the Poisson space of μ. We generalise this result in the context of a measure μ on a locally compact semigroup S, in particular establishing the existence of a Poisson space for non-separable groups. The proof is non-probabilistic, and depends on properties of projections on C(K)(K compact Hausdorff). We then show that if S is compact and the support of μ generates S, then the Poisson space associated with μ, is X, where X×G×Y is the Rees product representing the kernel of S.

A Characterisation of Locally Compact Amenable Subsemigroups

1980 ◽  
Vol 23 (3) ◽  
pp. 305-312 ◽  
Author(s):  
James C. S. Wong
Keyword(s):  
Compact Semigroup ◽  
Invariant Mean ◽  
Locally Compact ◽  
Characteristic Functional ◽  
Locally Compact Semigroup ◽  
Borel Measurable

AbstractIn this paper, we prove that if S is a locally compact semigroup and T a locally compact Borel measurable subsemigroup of S, then T has a topological left invariant mean if and only if there is a topological left T-invariant mean M on S such that M(xT) = 1, where xT is the characteristic functional of T in S.

On the Semigroup of Probability Measures of a Locally Compact Semigroup

1987 ◽  
Vol 30 (2) ◽  
pp. 142-146 ◽  
Author(s):  
James C.S. Wong
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Compact Semigroup ◽  
Continuous Functions ◽  
Convolution Semigroup ◽  
Probability Measures ◽  
Point Property ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Uniformly Continuous

AbstractWe show that a locally compact semigroup S is topological left amenable iff a certain space of left uniformly continuous functions on the convolution semigroup of probability measures M0(S) on S is left amenable or equivalently iff the convolution semigroup M0(S) has the fixed point property for uniformly continuous affine actions on compact convex sets.

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