Endogenous Measures and Refinement Dynamics on Finite {\sigma}-Algebra Systems

Paul Baird

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arXiv · 2604.27655

Endogenous Measures and Refinement Dynamics on Finite {\sigma}-Algebra Systems

Paul Baird

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Abstract

We study systems of {\sigma}-algebras ordered by refinement and introduce the notion of an endogenous probability measure, invariant under admissible refinement transformations. We prove existence and structural properties of such measures on finite systems and show how refinement operators induce a natural dynamical structure on the lattice of {\sigma}-algebras.

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Paul Baird. 2026-04-30. Endogenous Measures and Refinement Dynamics on Finite {\sigma}-Algebra Systems. https://arxiv.org/abs/2604.27655

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