We prove a pointwise ergodic theorem for averages over dilates of a compact submanifold for a measure-preserving $\mathbb{R}^d$-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.