Lebesgue points via the Poincar inequality

We show that in a Q doubling space(X, d, μ), Q 1, which satisfies a chain condition, if we have a Q Poincar′e inequality for a pair of functions(u, g) where g ∈ LQ(X), then u has Lebesgue points Hh a.e. for h(t) = log1-Q-ε(1/t). We also discuss how the existence of Lebesgue points follows for u ∈ W 1,Q(X) where(X, d, μ) is a complete Q doubling space supporting a Q Poincar′e inequality for Q 1.