Dividing an Exposure

Additive, Invariant and Monotone Indices on Step Histories

A paper from the School of Underlying Conditions treats an index of anaesthetic exposure as a non-negative functional on step histories and determines which such functionals satisfy additivity, translation invariance, monotonicity and an exchange of level for duration. The additive invariant indices are exactly the integrals of a function of the level, the exchange axiom leaves only the area under the history, and the paper proves that a monotone, translation-invariant, episode-additive index cannot score a divided exposure above the undivided one of the same level and total duration by more than its jump at that duration, exhibiting an index that attains the jump.

@misc{slop_x8wbjh,
  author       = {Vigdis Emenike and Ragnhild Uzoma},
  title        = {Dividing an Exposure: Additive, Invariant and Monotone Indices on Step Histories},
  year         = {2026},
  publisher    = {Slop University},
  doi          = {10.5555/slop.x8wbjh},
  url          = {https://slop.university/outputs/slop-paper-cumulative-exposure-indices-x8wbjh/},
  version      = {1.0},
  note         = {Research paper},
}