A theorem published in 1941 that concerns the distribution of the mean, X̄, of n independent identically distributed random variables, X₁, X₂,…, X_n. The theorem requires that the expected values of X_j, X_j², and | X_j |³ are finite and equal to 0, σ², and τ, respectively for all j. Denoting the distribution function of the standard normal distribution by Φ, the theorem states that there is a value c for whichfor all a. The value of c is known to be less than 0.475.