474 research outputs found
Representation of maxitive measures: an overview
Idempotent integration is an analogue of Lebesgue integration where
-maxitive measures replace -additive measures. In addition to
reviewing and unifying several Radon--Nikodym like theorems proven in the
literature for the idempotent integral, we also prove new results of the same
kind.Comment: 40 page
Metric Properties of the Fuzzy Sphere
The fuzzy sphere, as a quantum metric space, carries a sequence of metrics
which we describe in detail. We show that the Bloch coherent states, with these
spectral distances, form a sequence of metric spaces that converge to the round
sphere in the high-spin limit.Comment: Slightly shortened version, no major changes, two new references,
version to appear on Letters in Mathematical Physic
Convergence and quantale-enriched categories
Generalising Nachbin's theory of "topology and order", in this paper we
continue the study of quantale-enriched categories equipped with a compact
Hausdorff topology. We compare these -categorical compact
Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that
the presence of a compact Hausdorff topology guarantees Cauchy completeness and
(suitably defined) codirected completeness of the underlying quantale enriched
category
H\"older Error Bounds and H\"older Calmness with Applications to Convex Semi-Infinite Optimization
Using techniques of variational analysis, necessary and sufficient
subdifferential conditions for H\"older error bounds are investigated and some
new estimates for the corresponding modulus are obtained. As an application, we
consider the setting of convex semi-infinite optimization and give a
characterization of the H\"older calmness of the argmin mapping in terms of the
level set mapping (with respect to the objective function) and a special
supremum function. We also estimate the H\"older calmness modulus of the argmin
mapping in the framework of linear programming.Comment: 25 page
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