Kolmogorov–Arnold representation theorem

In real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function f : [ 0 , 1 ] n → R {\displaystyle f\colon [0,1]^{n}\to \mathbb {R} } can be represented as a superposition of continuous single-variable functions. The works of Vladimir Arnold and Andrey Kolmogorov established that if f is a multivariate continuous function, then f can be written as a finite composition of continuous functions of a single variable and the binary operation of addition.

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