Extreme convex set functions with finite carrier: General theory

摘要: Let @W={1,...,n} and P={X:[email protected][email protected]}. A mapping e : P->R^+ is a convex set function if e(@?)=0 e(S) + e(T)== 2. There certain subsystem of sets [email protected] such that m^@t(S)[email protected]"@t=e(S) (@[email protected]}, is, the S m^@t(S)[email protected]"@t(@[email protected]) maximal term in representation by m^1,...,m^@t @a"1,[email protected]"t.e called nondegenerate these subsystems determine measures uniquely it turns out nondegeneracy extremality are equivalent for @e ^1. Moreover, seen closely related to generalized version problem ''represent given integer @l >= o means weights g,...,g"r 0 via @s^r"@r="1a"@rg"@[email protected] coefficients a"@r satisfy 0=