Gnedenko–Kolmogorov limit theorem

Target entity: Gnedenko–Kolmogorov limit theorem
Context triple: [Boris Gnedenko, knownFor, Gnedenko–Kolmogorov limit theorem]

• A. Lindeberg–Feller central limit theorem
  The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
• B. Kolmogorov's law of the iterated logarithm
  Kolmogorov's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables between the law of large numbers and the central limit theorem.
• C. Berry–Esseen theorem
  The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
• D. Lévy’s continuity theorem
  Lévy’s continuity theorem is a fundamental result in probability theory that characterizes convergence in distribution of random variables via pointwise convergence of their characteristic functions.
• E. Khinchin–Kolmogorov theorem
  The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Gnedenko–Kolmogorov limit theorem
Target entity description: The Gnedenko–Kolmogorov limit theorem is a fundamental result in probability theory that characterizes the limiting distributions of properly normalized sums of independent random variables, generalizing the classical central limit theorem to stable laws.

• A. Lindeberg–Feller central limit theorem
  The Lindeberg–Feller central limit theorem is a general form of the central limit theorem that provides conditions under which sums of independent, not necessarily identically distributed random variables converge in distribution to a normal law.
• B. Kolmogorov's law of the iterated logarithm
  Kolmogorov's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables between the law of large numbers and the central limit theorem.
• C. Berry–Esseen theorem
  The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
• D. Lévy’s continuity theorem
  Lévy’s continuity theorem is a fundamental result in probability theory that characterizes convergence in distribution of random variables via pointwise convergence of their characteristic functions.
• E. Khinchin–Kolmogorov theorem
  The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
• F. None of above. chosen