Lindeberg-Feller theorems on Lie groups
Let \(G\) be a Lie group. A convolution semigroup \((\mu_t)_{t\geq 0}\) of nondegenerate measures is called a Gaussian semigroup if \(\lim_{t\to 0}t^{-1}\mu_t(G\setminus U)= 0\) for each neighborhood \(U\) of \(e\). A probability measure \(\mu\) on \(G\) is called a Gaussian measure if there exists a Gaussian semigroup \((\mu_t)_{t\geq 0}\) such that \(\mu_1= \mu\). The author obtains necessary and sufficient conditions for the triangular array \((\mu_{nl})_{l= 1,\dots, k_n;n\geq 1}\) of probability measures on \(G\) to converge to a Gaussian measure.
scientific article; zbMATH DE number 1309370