The natural best \(L^ 1\)-approximation by nondecreasing functions (Q1108509)

The authors discuss the natural best \(L_ 1\)-approximation to an integrable function f by the elements of an \(L_ 1\)-closed convex proximal set. When \(f\in L[0,1]\) and the approximating set is of all non- decreasing functions, they show that their result is an extension of known natural best \(L_ 1\)-approximation operator from \(\cup_{p>1}L_ p\) to \(L_ 1\). In the end, the authors discuss the case of isotonic approximation to a function of several variables.