On the Carathéodory superposition (Q1322639)

The paper deals with the Carathéodory superposition \(h(x)= f(x,g(x))\), where \((X,M,m)\) is a totally sigma finite measure space and \(Y\) is a metric space and \(g: X\to Y\). In sections I--IV there are studied conditions under which a function \(h\) is a derivative (with respect to some differentiation basis) and in the last section these results are applied to show that the Cauchy problem has at least one solution under very general assumptions.