2]) has

infimum value 0 but no minimum value in [[bar.

23 We implicitly assume that a positive

infimum in Equation 18 exists.

Taking the

infimum over [lambda] [member of] K in (?

For any two probability measures P and Q in M(S'), the Prohorov metric is defined as the

infimum of those positive [epsilon] for which the inequalities Q(b) [less than or equal to] P([b.

In other words, h reaches its

infimum where the function g([Rho]) [equivalent to] h(b = [[Rho].

It is also a lattice for this order, the

infimum and supremum being taken entrywise: max[(X, Y).

where the

infimum is taken over all decompositions of f of the form (2).

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and the

infimum is taken over all countable collection ([I.

where [disconjunction] if the supremum (or maximum) operator and [conjunction] the

infimum (minimum) operator and B(x) is the structuring element centered at point x.

From the lemma this

infimum is maximized by choosing x = 0.

This structure was used implicitely by Giraudo for constructing the Baxter Hopf algebra from the Baxter monoid as the

infimum of the sylvester monoid and its image under SchUtzenberger involution.

Exchanging

infimum and supremum in the last formula can easily be justified with standard methods in convex analysis; cf.