A note on absorption semigroups and regularity

TL;DR

This paper demonstrates that two different definitions of regularity in absorption semigroups are actually equivalent, clarifying a fundamental aspect of their theoretical framework.

Contribution

It establishes the equivalence of two approaches to defining regularity in absorption semigroups, resolving a conceptual ambiguity.

Findings

Two definitions of regularity are equivalent

Clarifies foundational aspects of absorption semigroup theory

Simplifies theoretical framework for absorption rates

Abstract

It is shown that, in the theory of absorption semigroups, two possible ways of defining regularity for absorption rates are in fact equivalent.