Gnedenko’s theorem in extreme value theory

Target entity: Gnedenko’s theorem in extreme value theory
Context triple: [Boris Gnedenko, knownFor, Gnedenko’s theorem in extreme value theory]

• A. 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.
• B. Cramér’s theorem in large deviations
  Cramér’s theorem in large deviations is a fundamental result in probability theory that characterizes the exponential decay rate of tail probabilities for sums of independent, identically distributed random variables via a convex rate function.
• C. Modern Probability Theory and Its Applications
  "Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
• D. Limit Laws for Sums of Independent Random Variables
  Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Gnedenko’s theorem in extreme value theory
Target entity description: Gnedenko’s theorem in extreme value theory is a fundamental result that characterizes all possible non-degenerate limit distributions for properly normalized maxima of independent, identically distributed random variables, forming the basis of modern extreme value analysis.

• A. 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.
• B. Cramér’s theorem in large deviations
  Cramér’s theorem in large deviations is a fundamental result in probability theory that characterizes the exponential decay rate of tail probabilities for sums of independent, identically distributed random variables via a convex rate function.
• C. Modern Probability Theory and Its Applications
  "Modern Probability Theory and Its Applications" is a foundational textbook by Emanuel Parzen that systematically develops modern probability theory and demonstrates its use in a wide range of statistical and applied contexts.
• D. Limit Laws for Sums of Independent Random Variables
  Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
• E. 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.
• F. None of above. chosen