AMEANBLE ACTION AND INVARIANT MEAN

Topologically Left Invariant Mean on Dual Semigroup Algebras

Invariant Mean Value Property and Harmonic Functions

We give conditions on the functions σ and u on R such that if u is given by the convolution of σ and u, then u is harmonic on R.

An Arithmetic and Geometric Mean Invariant

A positive real interval, [a, b] can be partitioned into sub-intervals such that sub-interval widths divided by sub-interval ”‘average”’ values remains constant. That both Arithmetic Mean and Geometric Mean ”‘average”’ values produce constant ratios for the same log scale is the stated invariance proved in this short note. The continuous analog is briefly considered and shown to have similar pr...

topologically left invariant mean on dual semigroup algebras

Invariant Empirical Bayes Confidence Interval for Mean Vector of Normal Distribution and its Generalization for Exponential Family

Based on a given Bayesian model of multivariate normal with  known variance matrix we will find an empirical Bayes confidence interval for the mean vector components which have normal distribution. We will find this empirical Bayes confidence interval as a conditional form on ancillary statistic. In both cases (i.e.  conditional and unconditional empirical Bayes confidence interval), the empiri...