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Article

Kalina, Martin
Expected values in the alternative set theory and their applications to some limit theorems. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 35 (1994), issue 1, pp. 169-179
MSC: 03E70, 03H05, 26E35, 60A99, 60F05, 60F99 | MR 1292592 | Zbl 0802.60023
Keywords:
alternative set theory; expected value; law of large numbers; central limit theorem
Summary:
This article presents an alternative approach to statistical moments within non-standard models and by the help of these moments some limit theorems are reformulated and proved.
References:
[K-Z] Kalina M., Zlatoš P.: Borel classes in AST. Measurability, cuts and equivalence. Comment. Math. Univ. Carolinae 30 (1989), 357-372. MR 1014135
[L] Loeb P.A.: Conversion from nonstandard to standard measure spaces and applications in probability theory. Trans. AMS 211 (1975), 113-122. MR 0390154 | Zbl 0312.28004
[N] Nelson E.: Radically Elementary Probability Theory. Princeton University Press Princeton (1987). MR 0906454 | Zbl 0651.60001
[V] Vopěnka P.: Mathematics in the Alternative Set Theory. Teubner Texte Leipzig (1979). MR 0581368
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