Saito, Masahiko What is nonstandard analysis? (Japanese) Zbl 0633.26010 Sûgaku 38, 133-149 (1986). This paper is a survey on nonstandard analysis. It contains three parts: the frames of nonstandard analysis (I.1-I.5), some applications (II.6- II.9), and nonstandard set theory (III.10). Particularly, some works of Japanese scholars are included. The goal of I.1 and I.2 is to give the basic concepts as Zermelo’s universes, transfer axiom and enlargement axiom. With these materials it is possible to define infinitesimal numbers. A further discussion (Robinson’s ultrafilter, ultrapower, LOS theorem, internal and external set, saturated model) is given in I.3-I.5. In II.7. the author proves the existence of Haar measure. Perhaps this proof is a new one. The Loeb measure theory which the author describes in II.9 is one of recent results of nonstandard analysis. In the last section, the author deals with a new set theory, Kawai’s NST theory [T. Kawai, Logic, Proc. Southeast Asian Conf., Singapore 1981, Stud. Logic Found. Math. 111, 55- 76 (1983; Zbl 0542.03046)]. Reviewer: Lie-Ren Sheng Cited in 1 Document MSC: 26E35 Nonstandard analysis 28E05 Nonstandard measure theory 03H05 Nonstandard models in mathematics Keywords:survey on nonstandard analysis; Zermelo’s universes; infinitesimal numbers; Haar measure; Loeb measure theory; Kawai’s NST theory Citations:Zbl 0542.03046 PDFBibTeX XMLCite \textit{M. Saito}, Sūgaku 38, 133--149 (1986; Zbl 0633.26010)