In this paper we show that the ball measure of non-compactness of a norm
bounded subset of an Orlicz modular space Lψ is equal to the limit of its
n-widths. We also obtain several inequalities between the measures of non￾compactness and the limit of the n-widths for modular bounded subsets of Lψ
which do not have ∆2-condition. Minimum conditions onψ to have such results
are specified and an example of such a function ψ is provided.