## Archive of posts in Mar, 2023

### 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.

- Categories: physics
- Tags: mathematical physics, statistical mechanics, functional analysis, measure theory, probability, long paper

### The core of a voting system is the intersection of Pareto sets

There is a very neat relation between the core (the set of proposals that defeats every proposal) of a voting system and the Pareto sets of the voters. Suppose there is a voting system of quota $q$, then the core is the intersection of all such sets: the Pareto set of $q$ of the voters.

- Categories: economics
- Tags: voting system, preference relation, pareto efficiency