Gordin, M. I. Extensions of dynamical systems and the method of martingale approximation. (Russian. English summary) Zbl 0868.60011 Zap. Nauchn. Semin. POMI 216, 10-19 (1994). Summary: Let \(T\) be a measure preserving transformation of a probability space \(({\mathcal X},{\mathcal F},\mu)\) and \(A\) be the generator of a \(\mu\)-symmetric Markov process with state space \(X\). Under the assumption that \(A\) is an “eigenvector” for \(T\), an extension of \(T\) is constructed in terms of \(A\). By means of this extension a version of the central limit theorem is proved via approximation by martingales. Cited in 1 Review MSC: 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) 60J35 Transition functions, generators and resolvents Keywords:measure preserving transformation; central limit theorem; approximation by martingales PDFBibTeX XMLCite \textit{M. I. Gordin}, Zap. Nauchn. Semin. POMI 216, 10--19 (1994; Zbl 0868.60011) Full Text: EuDML