Wehling's Theorem

Wehling’s Theorem addresses the mathematical structure of certain types of functions known as characteristic functions, which are used in probability theory to describe how random variables behave. The theorem states that if a characteristic function has specific properties—namely, being continuous and satisfying certain symmetry conditions—it uniquely determines the probability distribution of a random variable. In simple terms, Wehling’s Theorem assures that the way we can mathematically encode a random variable's behavior (via its characteristic function) is sufficient to fully understand and reconstruct that variable's underlying probability distribution.