Internal sets and internal functions in Colombeau theory

Abstract

Inspired by nonstandard analysis, we define and study internal subsets and internal functions in algebras of Colombeau generalized functions. We prove a saturation principle for internal sets and provide applications to Colombeau algebras.

References in corpus (2)

• Isomorphisms of algebras of Colombeau generalized functions
• Spherical completeness of the non-archimedean ring of Colombeau generalized numbers

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