We prove a pointwise ergodic theorem for averages over dilates of a compact submanifold for a measure-preserving Rd-action, under the assumption of exponential mixing. We also obtain error rates, giving explicit bounds on the speed of convergence. This has an application in multiplicative Diophantine approximation providing a partial analogue of Khintchine’s 0− 1 law. This is a joint work with Reynold Fregoli and Dmitry Kleinbock.