Lisäisyys

Lisäisyys, literally “additivity” in Finnish, is a term used to describe a property whereby a whole can be understood as the sum of its parts. It arises in mathematical definitions as well as in statistical and applied models, in science fields where combining components should yield a predictable aggregate result.

In mathematics, additivity means that a function or measure preserves the operation of addition. For a function f, this is expressed as f(a + b) = f(a) + f(b) for all a and b in the domain. In measure theory, a measure μ is finitely additive if μ(A ∪ B) = μ(A) + μ(B) when A and B are disjoint, and countably additive if this holds for any countable collection of disjoint sets. Probability measures are countably additive, ensuring that the probability of a union of disjoint events equals the sum of their probabilities.

In statistics and econometrics, additive models assume that the effect of each variable adds to the total response without interactions, as in y = α + ∑ β_i x_i + ε. Additivity is often contrasted with non-additive interactions, where combined effects differ from simple sums. In engineering and physics, the superposition principle is an expression of lisäisyys for linear systems, where the response to multiple stimuli equals the sum of the responses to each stimulus individually.

Related concepts include subadditivity, superadditivity, and multiplicativity. The term is chiefly used in mathematical and statistical contexts, with broader usage in disciplines that study how parts combine to form wholes.