PUB - Publikationen an der Universität Bielefeld

Given a finite set E and a map f : P(E) --> R boolean OR {-infinity}, we define f to be well-layered, if and only if for every map eta : E --> R and every finite sequency e(1), e(2), ..., e(i) is an element of E with # {e(1), ..., e(i)} = i and f({e(1), ..., e(j)}) + Sigma(k=1)(j) eta(e(k)) greater than or equal to f({e(1), ..., e(j-1),e}) + Sigma(k=1)(j-1) eta(e(k)) + eta(e) for all j = 1, ..., i and e is an element of E/{e(1), ..., e(j-1)}, one has f({e(1), ..., e(i)}) + Sigma(k=1)(i) eta(e(k)) greater than or equal to f (I) + Sigma(e is an element of I) eta(e) for every I subset of or equal to E with # (J/I) greater than or equal to 3 and with f(I) not equal -infinity or I = 0 and for every a is an element of J/I, there exists some b is an element of J/(I boolean OR {a}) with f (I boolean OR {a}) + f (J/{a}) less than or equal to f (I boolean OR {b}) + f (J/{b}) = -infinity for all subsets I' with i < # I' < # E. In addition, we provide some ''generic'' examples of well-layered maps related to P-adic geometry, and we indicate some interesting applications releated to control theory.