Borel–Kolmogorov paradox

Target entity: Borel–Kolmogorov paradox
Context triple: [Émile Borel, notableWork, Borel–Kolmogorov paradox]

• A. 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.
• B. Mazurkiewicz–Sierpiński paradox
  The Mazurkiewicz–Sierpiński paradox is a result in set-theoretic geometry showing that a sphere can be decomposed and reassembled in a counterintuitive way, illustrating the existence of paradoxical decompositions similar to the Banach–Tarski paradox.
• C. Kolmogorov axioms
  The Kolmogorov axioms are the standard mathematical foundation of probability theory, formalizing probabilities as measures on a sigma-algebra that satisfy non-negativity, normalization, and countable additivity.
• D. Banach–Tarski paradox
  The Banach–Tarski paradox is a theorem in set-theoretic geometry stating that a solid ball in 3‑dimensional space can be decomposed into finitely many non-measurable pieces and reassembled into two identical copies of the original ball, highlighting counterintuitive consequences of the axiom of choice.
• E. St. Petersburg paradox
  The St. Petersburg paradox is a famous problem in probability theory and economics that highlights how a lottery with an infinite expected payoff can still attract only a finite price from rational gamblers, challenging traditional notions of expected value and decision-making under risk.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Borel–Kolmogorov paradox
Target entity description: The Borel–Kolmogorov paradox is a famous example in probability theory showing that conditional probabilities on events of measure zero can be ambiguous without specifying the underlying limiting procedure or σ-algebra.

• A. 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.
• B. Mazurkiewicz–Sierpiński paradox
  The Mazurkiewicz–Sierpiński paradox is a result in set-theoretic geometry showing that a sphere can be decomposed and reassembled in a counterintuitive way, illustrating the existence of paradoxical decompositions similar to the Banach–Tarski paradox.
• C. Kolmogorov axioms
  The Kolmogorov axioms are the standard mathematical foundation of probability theory, formalizing probabilities as measures on a sigma-algebra that satisfy non-negativity, normalization, and countable additivity.
• D. Banach–Tarski paradox
  The Banach–Tarski paradox is a theorem in set-theoretic geometry stating that a solid ball in 3‑dimensional space can be decomposed into finitely many non-measurable pieces and reassembled into two identical copies of the original ball, highlighting counterintuitive consequences of the axiom of choice.
• E. St. Petersburg paradox
  The St. Petersburg paradox is a famous problem in probability theory and economics that highlights how a lottery with an infinite expected payoff can still attract only a finite price from rational gamblers, challenging traditional notions of expected value and decision-making under risk.
• F. None of above. chosen