The conic property for vector measure market games

We prove that every continuous value on a space of vector measure market games $$Q$$ Q , containing the space of nonatomic measures $$NA$$ N A , has the conic property, i.e., if a game $$v\in Q$$ v ∈ Q coincides with a nonatomic measure $$\nu $$ ν on a conical diagonal neighborhood then $$\varphi (v)=\nu $$ φ ( v ) = ν . We deduce that every continuous value on the linear space $$\fancyscript{M}$$ M , spanned by all vector measure market games, is determined by its values on $$\fancyscript{L}\fancyscript{M}$$ L M - the space of vector measure market games which are Lipschitz functions of the measures. Copyright Springer-Verlag Berlin Heidelberg 2015