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Regularity Conditions—Christensen Measurability

  • Palaniappan Kannappan
Chapter
Part of the Springer Monographs in Mathematics book series (SMM)

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).

Keywords

Functional Equation Topological Space Regularity Condition Continuous Solution Regular Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterloo ONCanada

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