  Our work builds on known results for k-uniform hypergraphs including the
existence of limits, a Regularity Lemma and a Removal Lemma. Our main tool here
is a theory of measures on ultraproduct spaces which establishes a
correspondence between ultraproduct spaces and Euclidean spaces. First we show
the existence of a limit object for convergent sequences of relational
structures and as a special case, we retrieve the known limits for graphs and
digraphs. Then we extend this notion to finite models of a fixed universal
theory. We also state and prove a Regularity Lemma and a Removal Lemma. We will
discuss connections between our work and Razborov's flag algebras as well.
