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Abstract <p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • Anh Nguyen Ha Hoai,
  • Hoa Nguyen Thi Khanh,
  • Thuy Le Hoang,
  • Trang Nguyen Linh

摘要

Abstract

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.