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

Key Points

• The aim is to establish a mean convergence theorem for triangular arrays of independent random vectors in Hilbert spaces.
• Developed a mean convergence theorem for triangular arrays
• Analyzed rowwise and pairwise independence in random vectors
• Improved the Kolmogorov–Feller weak law results
• Provided conditions under which mean convergence occurs
• Demonstrated that mean convergence is a stronger outcome than convergence in probability