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The 40 pages that link to Characteristic function, each with the reason it gives.

• SetRelated: It represents set membership numerically.

• Probability distributionRelated: Unlike a moment-generating function, it exists for every probability distribution.

• Central limit theoremRelated: Convergence of characteristic functions provides a standard proof route for the theorem.

• Power setRelated: Each subset corresponds to a binary inclusion pattern on the original set.

• Independent and identically distributed random variablesRelated: Products of characteristic functions describe sums of independent copies and support limit arguments.

• Probability mass functionRelated: It encodes a distribution through a transform rather than listing its point probabilities.

• Cantor's theoremRelated: It represents each subset as a function, enabling the diagonal proof.

• Convergence in distributionRelated: Convergence of characteristic functions can establish convergence in distribution under standard conditions.

• Dominated convergence theoremRelated: Dominated convergence helps establish continuity and convergence properties of characteristic functions.

• Partial functionRelated: Its domain can be restricted to a subset, yielding a partial membership test.

• DiagonalizationRelated: It turns subsets into sequences of bits that can be altered along the diagonal.

• MultisetRelated: Multisets use the analogous count function, whose values can exceed one.

• Cauchy distributionRelated: The Cauchy characteristic function is an exponential in absolute frequency, unlike a Gaussian’s quadratic exponent.

• Gaussian distributionRelated: The Gaussian’s characteristic function makes sums of independent Gaussians straightforward to analyze.

• Independent random variablesRelated: Joint characteristic functions factor into marginal ones exactly when the variables are independent.

• Set-builder notationRelated: It encodes the same membership test that a set-builder condition expresses.

• Theory of Games and Economic BehaviorRelated: It encodes the coalition opportunities used in the book’s cooperative analysis.

• Cooperative game theoryRelated: It encodes coalition-making possibilities in the transferable-utility model.

• Sierpiński spaceRelated: A subset's characteristic map is continuous precisely when the selected subset is open, with suitable value assignment.

• Boolean ringRelated: Characteristic functions translate set operations into multiplication and addition in the two-element ring.

• Membership relationRelated: It encodes membership as a binary-valued function when a surrounding domain is fixed.

• Equality relationRelated: For a fixed domain, it can encode equality by returning 1 exactly on diagonal pairs.

• Multivariate normal distributionRelated: Its closed form compactly determines the multivariate normal distribution, including singular cases.

• Paul LévyRelated: Lévy used characteristic functions to characterize distributions and prove limit results.

• Random vectorRelated: Its multivariate version uniquely determines a random vector's distribution.

• Computable setRelated: Computability of this function is equivalent to deciding membership in the set.

• Berry–Esseen theoremRelated: Esseen’s approach uses characteristic functions to translate moment information into distributional error bounds.

• CodeRelated: It converts a set into a numerical representation.

• Bondareva–Shapley theoremRelated: Its coalition values are the data tested by balancedness and the core.

• Cramér–Wold theoremRelated: Projection laws determine the multivariate characteristic function along every line through the origin.

• Erdős–Kac theoremRelated: Characteristic functions provide a route from prime-divisibility estimates to convergence in distribution.

• Blum axiomsRelated: The bounded-value predicate can be represented as a total computable characteristic function.