1. Doob, J. L.: Stochastic Processes. New York 1953.
2. Dobrushin, R. L.: Funct. Anal. Appl.2, 302 (1968) (Section 3, Theorem 2) see also Ruelle, D. Ref. [4] below.
3. This result, in the particular caser=1, was proven by F. Spitzer: Am. Math. Monthly, February, 142 (1971) and, independently, by M. B. Averintzer (see Reference at p. 143 of Spitzer's paper). The general result is clearly implicitely proved in Griffiths, R. B., Ruelle, D.: Commun. math. Phys.23, 169 (1971) (Section 3, p. 173). An explicit proof can be found in the paper by Del Grosso, G., Tesei, A.: The local central limit theorem for Gibbs' procesus, preprint, Istituto di Matematico, Roma.
4. Ruelle, D.: Commun. math. Phys.9, 267 (1968).
5. Friedman, N. A., Ornstein, D. S.: Adv. Math.5, 365 (1970). See also P. Shields: The theory of Bernoulli shifts, Preprint, Univ. of California, Math. dept., Berkeley.