The paper presents a central limit theorem for a sequence of dependent random variables, assuming the usual conditions on second and 2 + δ order moments and a strong mixing condition. The strong mixing condition is defined in terms of the distance between sets of indices and a function f(n) that decreases to zero as n approaches infinity. The theorem formalizes an intuitive notion from A. Markoff's work, suggesting that the central limit theorem holds for dependent variables if they behave more like independent variables as they are separated. The strong mixing condition is a more intuitive formalization of this idea and is also related to the mixing conditions in ergodic theory. The central limit theorem states that under the given assumptions, the normalized sum \( S_n = \frac{1}{\sqrt{kh(p_n)}} \sum_{j=1}^n X_j \) is asymptotically normally distributed. The proof involves detailed calculations and inequalities, including the use of Lemmas 1 and 2, to show that the sum of certain partial sums of the random variables is asymptotically normal. The conditions on the sequences \( k, p_n, q_n \) are chosen to ensure that the mixing condition and the moment conditions are satisfied, leading to the asymptotic normality of the normalized sum \( S_n \). The result includes the findings of Höffding and Robbins and suggests further interest in the strength of the strong mixing condition compared to the ordinary mixing condition in strictly stationary processes.The paper presents a central limit theorem for a sequence of dependent random variables, assuming the usual conditions on second and 2 + δ order moments and a strong mixing condition. The strong mixing condition is defined in terms of the distance between sets of indices and a function f(n) that decreases to zero as n approaches infinity. The theorem formalizes an intuitive notion from A. Markoff's work, suggesting that the central limit theorem holds for dependent variables if they behave more like independent variables as they are separated. The strong mixing condition is a more intuitive formalization of this idea and is also related to the mixing conditions in ergodic theory. The central limit theorem states that under the given assumptions, the normalized sum \( S_n = \frac{1}{\sqrt{kh(p_n)}} \sum_{j=1}^n X_j \) is asymptotically normally distributed. The proof involves detailed calculations and inequalities, including the use of Lemmas 1 and 2, to show that the sum of certain partial sums of the random variables is asymptotically normal. The conditions on the sequences \( k, p_n, q_n \) are chosen to ensure that the mixing condition and the moment conditions are satisfied, leading to the asymptotic normality of the normalized sum \( S_n \). The result includes the findings of Höffding and Robbins and suggests further interest in the strength of the strong mixing condition compared to the ordinary mixing condition in strictly stationary processes.