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. l_p
• The value of m does not depend on the order of coordinates; i.e.:
  m( ..x_i-1,x_i, x_i+1,..., x_j-1,x_j, x_j+1,.. ) = m( ..x_i-1,x_j, x_i+1,..., x_j-1,x_i, x_j+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