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über die Definition von effektiven Zufallstests
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  • Published: December 1970

über die Definition von effektiven Zufallstests

Teil I

  • Claus -Peter Schnorr1 

Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete volume 15, pages 297–312 (1970)Cite this article

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Summary

A new approach is made to characterize random sequences by introducing the concept of effective test function. A test function is a computable function that associates to each finite sequence a positive real number which indicates the extend to which the sequence stands the stochasticity test under consideration. Each test function has a corresponding set of measure zero, namely the set that consists of all infinite sequences which do not stand the test. This type of constructive null set is a generalization of the set of measure zero as defined by Brouwer. We will prove that test functions and sets of measure zero in the sense of Brouwer imply equivalent definitions of random sequences.

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Literatur

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  4. Heyting, A.: Intuitionism, an introduction. Amsterdam: North-Holland 1956.

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  7. Schnorr, C. P.: Eine Bemerkung zum Begriff der zufÄlligen Folge. Z. Wahrscheinlichkeitstheorie verw. Geb. 14, 27–35 (1969).

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Authors and Affiliations

  1. Institut für Angewandte Mathematik der UniversitÄt des Saarlandes, D-6600, Saarbrücken 15

    Claus -Peter Schnorr

Authors
  1. Claus -Peter Schnorr
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Additional information

Die Arbeit stellt einen Teil der Habilitationsschrift dar, die der Mathematisch-Naturwissenschaftlichen FakultÄt der UniversitÄt des Saarlandes vom Verfasser vorgelegt wurde.

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Cite this article

Schnorr, C.P. über die Definition von effektiven Zufallstests. Z. Wahrscheinlichkeitstheorie verw Gebiete 15, 297–312 (1970). https://doi.org/10.1007/BF00533301

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  • Received: 12 June 1969

  • Issue Date: December 1970

  • DOI: https://doi.org/10.1007/BF00533301

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