Nearconstant

Nearconstant is a descriptive term used across mathematics, statistics, and applied sciences to denote quantities that change very little across a specified domain. It is typically used when a variable or function can be treated as effectively constant within the context of a model or analysis.

In a deterministic setting, a function f is near-constant on a domain D if its range is contained in a small interval. Formally, there exists epsilon > 0 such that sup_{x in D} f(x) - inf_{x in D} f(x) <= epsilon. In a probabilistic setting, a random variable X is near-constant if its variance is small relative to its mean, or if the coefficient of variation CV = std(X)/E[X] is small.

Applications include simplifying equations in perturbation theory, physics, and economics when variations are negligible compared to the scales of interest. In time-series and signal processing, near-constant signals can be approximated by their mean over a window, or by low-order models.

Common measures of near-constancy are the range, variance, standard deviation, or the L-infinity norm of the derivative; the choice depends on context. Related concepts include constant functions, quasi-constant, and slowly varying functions.