Archive of posts with tag “functional analysis”
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How Pareto optimizations of distances relate to closed convex hulls
The distance preference relation is the preference relation over a metric space where points nearer to the ideal point are preferred. Suppose there are some agents with distance preference relations over a real normed space, then the (weak/strong) Pareto set of them may contain or be contained by the closed convex hull of their ideal points. This article attempts to completely classify normed spaces based on whether the property holds for all finite sets, all compact sets, all bounded sets, or all sets of ideal points. Several characterizations in infinite dimensions remain open. -
A measure-theoretic formulation of statistical ensembles (part 2)
For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms. -
A measure-theoretic formulation of statistical ensembles (part 1)
For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.
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