Clarify properties of existing quasiprobability majorization proposals on infinite measure spaces

Determine whether the definitions for majorization of quasiprobability distributions over infinite measure spaces proposed by de2024continuous inherit the core properties known in the finite-measure case, such as the equivalence between characterizations based on Lorenz curves, stochastic operators, Schur-convex functionals, and ordered rearrangements.

Background

The authors note that previous works have proposed definitions of majorization for quasiprobabilities over infinite measure spaces. However, due to challenges such as the infinite-plateau effect, it is nontrivial to ensure these proposals retain the standard desirable features established in finite-measure settings.

Motivated by this gap, the present paper introduces a new framework that does admit equivalent characterizations. Nonetheless, the status of the earlier proposals remains explicitly stated as unclear.