Kolmogorov's law of the iterated logarithm

Target entity: Kolmogorov's law of the iterated logarithm
Context triple: [Khinchin's law of the iterated logarithm, isSpecialCaseOf, Kolmogorov's law of the iterated logarithm]

• A. Khinchin's law of the iterated logarithm
  Khinchin'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 on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
• B. Kolmogorov zero–one law
  The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
• C. Donsker's invariance principle
  Donsker's invariance principle is a fundamental result in probability theory stating that suitably normalized random walks converge in distribution to Brownian motion, providing a functional central limit theorem.
• D. 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.
• E. Borel–Cantelli lemmas
  The Borel–Cantelli lemmas are fundamental results in probability theory that characterize when events occur infinitely often or only finitely often, based on the convergence or divergence of the sum of their probabilities.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Kolmogorov's law of the iterated logarithm
Target entity description: 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.

• A. Khinchin's law of the iterated logarithm
  Khinchin'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 on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
• B. Kolmogorov zero–one law
  The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
• C. Donsker's invariance principle
  Donsker's invariance principle is a fundamental result in probability theory stating that suitably normalized random walks converge in distribution to Brownian motion, providing a functional central limit theorem.
• D. 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.
• E. Borel–Cantelli lemmas
  The Borel–Cantelli lemmas are fundamental results in probability theory that characterize when events occur infinitely often or only finitely often, based on the convergence or divergence of the sum of their probabilities.
• F. None of above. chosen