Abstract

Necessary and sufficient conditions for the validity of the central limit theorem for densities are considered with respect to the norms in Orlicz spaces. The obtained characterization unites several results due to Gnedenko and Kolmogorov (uniform local limit theorem), Prokhorov (convergence in total variation) and Barron (entropic central limit theorem).

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Topics from this Paper

  • Limit Theorem For Densities
  • Convergence In Total Variation
  • Orlicz Spaces
  • Local Limit Theorem
  • Limit Theorem
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