Abstract
Regularity conditions and Christensen measurability and its applications are treated in this chapter. Conditions such as boundedness, monotonicity, measurability, continuity at a point, continuity, the Baire property, integrability, differentiability, and analyticity, for example, are called regularity conditions. To solve functional equations, it was customary to assume a rich regularity property like differentiability and reduce a functional equation to a differential equation and solve it. The trend for quite some time has been to solve functional equations under weaker regularity conditions like integrability or measurability or no regularity condition at all (solve algebraically).
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