Bernstein’s theorem in probability theory

Target entity: Bernstein’s theorem in probability theory
Context triple: [Sergei Natanovich Bernstein, notableConcept, Bernstein’s theorem in probability theory]

• A. Isserlis’ theorem in probability theory
  Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
• 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. 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.
• D. 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.
• E. Bernstein theorem
  Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Bernstein’s theorem in probability theory
Target entity description: Bernstein’s theorem in probability theory is a result that characterizes when a sequence of random variables converges in distribution to a normal (Gaussian) law under certain moment or independence conditions.

• A. Isserlis’ theorem in probability theory
  Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
• 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. 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.
• D. 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.
• E. Bernstein theorem
  Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
• F. None of above. chosen