There is a
resource represented by a set
C. There is a
valuation over the resource, defined as a continuous
measure V: 2^C\to \mathbb{R}. The measure
V can be represented by a
value-density function v: C\to \mathbb{R}. The value-density function assigns, to each point of the resource, a real value. The measure
V of each subset
X of
C is the integral of
v over
X. A valuation
V is called
piecewise-constant, if the corresponding value-density function
v is a
piecewise-constant function. In other words: there is a partition of the resource
C into finitely many regions,
C1,...,
Ck, such that for each
j in 1,...,
k, the function
v inside
Cj equals some constant
Uj. A valuation
V is called
piecewise-uniform if the constant is the same for all regions, that is, for each
j in 1,...,
k, the function
v inside
Cj equals some constant
U. == Generalization ==