"Natural" Conditions on used Functions
We always may assume the following "natural conditions " to the used functions:
- m, D and e are continuous, in most cases they are also differentable.
- m > 0. Often m is a norm, e.g. lp
- The value of m does not depend on the order of coordinates; i.e.:
xj+1,.. ) =
- D( p1,p2,p3 ) > 0
for each positive orientated triangle p1,p2,p3.
- In most cases D has a kind of "monotony":
Among all triangles with given base AB the isoscele has extremal value
(valued by D).
- e( p1,p2 ) > 0,
equality if and only if p1 = p2