A general principle for limit theorems in finitely additive probability: The dependent case
In Trans. Am. Math. Soc. 273, 541-550 (1982; Zbl 0507.60012), the author has proved a general principle, i.e. almost all limit theorems that are true in countably additive probability theory are also true in finitely additive probability theory in the independent case. Here, this result is generalized to the dependent case on the same line. More precisely, given a sequence \(\{Y_ n\}\) of random variables on a finitely additive probability space, one can construct a sequence \(\{X_ n\}\) of random variables on a countably additive probability space such that a convergence in probability or in distribution type limit theorem holds for \(\{Y_ n\}\) iff it holds for \(\{X_ n\}\). If the sequence \(\{Y_ n\}\) satisfies further an additional condition, the same is true for a.s. convergence type limit theorems.
scientific article; zbMATH DE number 4040935