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The aso theory developed in Chapters 8 - 12 presumes that the tan-
gent cones are linear spaces. In the present chapter we collect a
few natural examples where the tangent cone fails to be a linear
space. These examples are to remind the reader that an extension of
the theo- ry to convex tangent cones is wanted. Since the results
are not needed in the rest of the book, we are more generous ab out
regularity condi- tions. The common feature of the examples is the
following: Given a pre- order (i.e., a reflexive and transitive
order relation) on a family of p-measures, and a subfamily i of
order equivalent p-measures, the fa- mily ~ consists of p-measures
comparable with the elements of i. This usually leads to a (convex)
tangent cone 1f only p-measures larger (or smaller) than those in i
are considered, or to a tangent co ne con- sisting of a convex cone
and its reflexion about 0 if both smaller and larger p-measures are
allowed. For partial orders (i.e., antisymmetric pre-orders),
ireduces to a single p-measure. we do not assume the p-measures in
~ to be pairwise comparable.
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