Rechtscontinu

Rechtscontinu, sometimes written as rechtskontinuität or rechtskontinuierlich in German-language texts, refers to the mathematical property of right-continuity. A function f is called rechtskontinuierlich at a point x0 if the right-hand limit exists and equals the function value, that is lim_{h→0+} f(x0 + h) = f(x0). If this holds for every x0 in the domain, the function is rechtscontinu on its domain.

In analysis and topology, rechtscontinuity is a one-sided form of continuity. A function can be rechtskontinuierlich everywhere while still failing to be continuous at some points if the left-hand limits do not match. An example is the Heaviside step function H, defined by H(x) = 0 for x < 0 and H(x) = 1 for x ≥ 0; H is rechtskontinuierlich at every point, including 0, but is not continuous at 0 because the left-hand limit is 0 while the right-hand limit and value are 1.

In probability theory, right-continuous sample paths are common and often paired with left limits in the cadlag (RCLL) class of processes, meaning the paths are right-continuous with left limits. This property is important for defining filtrations, stopping times, and convergence results in stochastic calculus.

See also left-continuity, cadlag (continue a droite, limites à gauche), and monotone functions, which may exhibit only one-sided continuity properties.