We consider a local minimizer of the classical problem of the calculus of variations, where the Lagrangian is just Borel measurable. When is real valued, we merely assume a local Lipschitz condition on with respect to t, allowing to be discontinuous and nonconvex in x or . In the case of an extended valued Lagrangian, we impose the lower semicontinuity of the Lagrangian, and a condition on the effective domain of the Lagrangian. We use a recent variational Weierstrass type inequality to show that the minimizers satisfy a relaxation result and an Erdmann – Du Bois-Reymond convex inclusion which, remarkably, holds whenever is autonomous and just Borel. Under a growth condition, weaker than superlinearity, we infer the Lipschitz continuity of minimizers.