Functions in Llocp [0, ∞) where 1 ≤ p ≤ ∞ can be considered as inputs to linear systems. However, hysteresis operators of Preisach type have only been defined on much smaller space of regulated (or Baire) functions. In this paper, we re-define Play operators so that they are well defined for real valued measurable functions. We show that this definition coincides with the older definition for continuous and regulated functions on an interval. Domain extension of hysteresis operators of Preisach type to real, Lebesgue measurable functions is then obtained in the standard manner using the re-defined Play operators.
- Hysteresis operators of Preisach type
- Lebesgue measurable functions