additivisuus

Additivity, known in Finnish as additivisuus, is a property whereby a quantity for a combined system equals the sum of the quantities for its parts when the parts do not interact. It is central in mathematics and related fields, where it is often expressed by an equation such as f(x+y)=f(x)+f(y) for all x,y in the domain, or by the property μ(A∪B)=μ(A)+μ(B) for disjoint sets A and B.

In mathematics, an additive function satisfies f(x+y)=f(x)+f(y). A common example is f(x)=kx. A measure μ is additive if μ(A∪B)=μ(A)+μ(B) for disjoint A,B; Lebesgue measure is additive. Finite additivity refers to finite unions; sigma-additivity extends to countable unions and is the standard axiom for probability measures.

In probability and statistics, additivity underpins decomposing probabilities and expectations, and in additive models Y = μ + f1(X1) + f2(X2) + ... expresses the idea that effects sum. In physics and thermodynamics, extensive quantities such as energy and mass are additive for independent subsystems; in economics, some utilities or costs are modeled as additive across goods.

Non-additive frameworks exist where interaction effects occur, such as non-additive probabilities (capacities), non-additive measures, or nonlinear models; these generalize or relax additivity. Additivity is thus a foundational, but not universal, principle across sciences.