Separation of Marginal and Joint Totalizability

Statement

There exists a downward-closed reconstruction system that is finitely rectangularly admissible, sourcewise totalizable, and demandwise totalizable, but not jointly totalizable.

Meaning and scope

The proof uses coordinate demands on and finite-dimensional permitted carriers. The required finite dimension is ; the doubly totalized context would require an injective map from an infinite-dimensional space into a finite-dimensional one.

Source

Paper 3, Theorem 2.2. Frozen manuscript — research note, not peer reviewed.