Let X_n;n ≥1 be a sequence of stationary associated random variables having a common marginal density function f (x). Let  , be a sequence of Borel-measurable functions defined on R². Let   be the empirical density function. Here we study a set of sufficient conditions under which the probability   at an exponential rate as n → ∞ where the rate possibly depends on ε, δ and f and [a, b] is a finite or an infinite interval.