Illinois Journal of Mathematics

An elementary nonstandard proof of Stone's representation theorem

Bernard Brunet

Full-text: Open access


A neat nonstandard proof of Stone's representation theorem is given. Improving on previous proofs (Loeb [5], Brunet [2]), it uses the remarkably simple fact that infinitesimal members of a filter on $X$, in any enlargement, are always compact for a natural topology on ${}^{\ast}X$.

Article information

Illinois J. Math., Volume 35, Issue 2 (1991), 312-315.

First available in Project Euclid: 19 October 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46E10: Topological linear spaces of continuous, differentiable or analytic functions
Secondary: 03H05: Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05] 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46S20: Nonstandard functional analysis [See also 03H05] 54J05: Nonstandard topology [See also 03H05]


Brunet, Bernard. An elementary nonstandard proof of Stone's representation theorem. Illinois J. Math. 35 (1991), no. 2, 312--315. doi:10.1215/ijm/1255987899.

Export citation