Regularly Varying Functions and the Principle of Equicontinuity

摘要

The concept of regularly varying functions is extended from real functions of a real variable to mappings of one topological group with a filter into another. The classical results on regularly varying functions are generalized, and one of these generalizations contains as a particular case the equicontinuity principle (or Banach-Steinhaus theorem). In the case of regularly varying functions of n real variables, the representation theorem is given. (Author)