absolute convergence: Meaning and Definition of

ab'solute conver'gence

1. the property of an infinite series in which the series formed by replacing each term in the original series with its absolute value converges. Cf. conditional convergence.
2. the property of a sequence of functions in which the series whose terms are the successive differences of the elements of the sequence exhibits absolute convergence.
3. the property of an improper integral in which the integral formed by replacing the integrand by its absolute value converges. Also called