Decomposition of multivariate functions. (English) Zbl 0789.54012
Summary: Given a bivariate function defined on some subset of the Cartesian product of two sets, it is natural to ask when that function can be decomposed as the sum of two univariate functions. In particular, is a pointwise limit of such functions itself decomposable? At first glance this might seem obviously true but, as we show, the possibilities are quite subtle. We consider the question of existence and uniqueness of such decompositions for this case and for many generalizations to multivariate functions and to cases where the sets and functions have topological or measure theoretic structure.
MSC:
54C05 | Continuous maps |
05C38 | Paths and cycles |
08A45 | Equational compactness |
28A20 | Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence |