his study is devoted to a test of theoretical results for the relation between the correlation function of turbulent velocity fluctuations obtained by Lagrangian and Eulerian sampling, respectively. The comparison is based on direct numerical simulations of the two-dimensional, incompressible Euler equations using a double periodic, fully de-aliased, high resolution spectral code. It is found that the theoretical expression for the Lagrangian correlation function estimates the simulated correlation function quite well, whereas the theoretical Eulerian one-point velocity correlation deviates significantly from the simulated one. The simulations do, however, confirm that the Eulerian integral timescale (T "SUB E" ) is larger than the Lagrangian integral timescale (T "SUB L" ), as predicted by the theory.