Title: Uniform pointwise ergodic theorems via ultraproducts

Abstract: We take a new point of view on weighted pointwise ergodic theorems by viewing the sequence (f(Tnx))n >= 1 as a vector in an ultraproduct space. This point of view allows us to directly transfer mixing properties of the underlying transformation to mixing properties of a shift operator on the ultraproduct space. In this new context, weighted pointwise ergodic theorems correspond to identifying functionals in the dual space that annihilate the starting vector. This allows us to not only recover the uniform Wiener-Wintner theorem of Lesigne, but to also prove a uniform pointwise ergodic theorem for ergodic, mild mixing, and strong mixing measure preserving transformations. Furthermore, our methods are general enough to apply to any L1-L\infty contraction on a Bochner space Lp(X,\mu;E) constructed from a reflexive Banach space .