A Mean Convergence Theorem for Triangular Arrays of Rowwise and Pairwise Independent Random Vectors in Hilbert Spaces

This paper establishes a mean convergence theorem for triangular arrays of rowwise and pairwise independent random vectors taking values in a real separable Hilbert space. The main result provides an improvement of the sufficient part of the Kolmogorov–Feller weak law of large numbers by establishing mean convergence instead of convergence in probability.