Nonthin

Nonthin is the negation of thin, used in both everyday language and specialized mathematical contexts. In general English, nonthin describes something that is not slender or not of small width and is used as the opposite of thin in physical descriptions or designations of materials, fabrics, or objects.

In mathematics, nonthin appears as a relative term within the broader concept of thinness. The adjective thin, and its negation nonthin, are employed in potential theory, harmonic analysis, and complex analysis to classify how a set behaves near a point. The notion of thinness describes a certain deficiency or obstruction in the approach of functions or measures to a boundary point. A set is said to be nonthin at a point when it does not exhibit this obstruction according to the relevant theory. While the precise technical definition varies by context, nonthinness generally signals that the set does not prevent certain boundary behaviors, extension properties, or harmonic measure considerations that would occur if the set were thin.

Because thinness is a technical and context-dependent concept, the term nonthin is not universally standardized outside its specific field. Readers encountering nonthin are typically referred to the particular definitions within potential theory, complex analysis, or the study of harmonic functions for exact criteria and implications.

See also: thin set, potential theory, harmonic measure, removable singularities, boundary regularity.