  A common problem in various applications is the additive decomposition of the
output of a function with respect to its input variables. Functions with binary
arguments can be axiomatically decomposed by the famous Shapley value. For the
decomposition of functions with real arguments, a popular method is the
pointwise application of the Shapley value on the domain. However, this
pointwise application largely ignores the overall structure of functions. In
this paper, axioms are developed which fully preserve functional structures and
lead to unique decompositions for all Borel measurable functions.
