A Mixing Condition for Extreme Left Invariant Means

Topologically left invariant means on semigroup algebras

Let M(S) be the Banach algebra of all bounded regular Borel measures on a locally compact Hausdorff semitopological semigroup S with variation norm and convolution as multiplication. We obtain necessary and sufficient conditions for M(S)∗ to have a topologically left invariant mean.

A New Mixing Condition

In this paper a new mixing condition for sequences of random variables is considered. This mixing condition is termed γ-mixing. Whereas mixing conditions such as α-mixing are typically defined in terms of entire σ-fields of sets generated by random variables in the distant past and future, γ-mixing is defined in terms of a smaller class of sets: the finite dimensional cylinder sets. This leads ...

SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

Mixing Invariant Densities

| For many chaotic systems there appears to be a single asymptotic distribution describing the frequency with which almost all trajectories visit diierent regions of state space. Such a distribution is commonly called the \physical" invariant measure or \natural" invariant measure of the system. Consider the evolution of a cluster of initial conditions under the action of the system. This clust...

Topologically Left Invariant Mean on Dual Semigroup Algebras