Independence Definition for Sequential Random Events establishes that two events within a sample space are statistically independent if and only if the occurrence probability of one event remains constant regardless of whether the second event has occurred, mathematically formalized as P(A ∩ B) = P(A) × P(B). This concept operates strictly within the domain of measure-theoretic probability theory as a fundamental axiom governing stochastic processes where historical outcomes exert no causal or informational influence on future trials. It serves as the critical theoretical delimiter separating Markovian and ergodic systems from those characterized by autocorrelation or memory effects in sequential data streams.
Prerequisite chain context: requires Sample Space Construction for Random Experiments.