### Abstract

This paper deals with the duality between Wiener measure and Baire category on c^{1} _{0}, the set of continuous functions f:[0, 1] → [0, 1] endowed with the supremum norm. We prove that some properties shared by a residual set of continuous functions, e.g. the typical level set structure, and the existence of periodic points of order 3 hold a.e. with respect to the Wiener measure.

Original language | English |
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Pages (from-to) | 455-463 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 106 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1989 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Some dual statements concerning wiener measure and baire category.** / Simon, K.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 106, no. 2, pp. 455-463. https://doi.org/10.1090/S0002-9939-1989-0961409-6

}

TY - JOUR

T1 - Some dual statements concerning wiener measure and baire category

AU - Simon, K.

PY - 1989

Y1 - 1989

N2 - This paper deals with the duality between Wiener measure and Baire category on c1 0, the set of continuous functions f:[0, 1] → [0, 1] endowed with the supremum norm. We prove that some properties shared by a residual set of continuous functions, e.g. the typical level set structure, and the existence of periodic points of order 3 hold a.e. with respect to the Wiener measure.

AB - This paper deals with the duality between Wiener measure and Baire category on c1 0, the set of continuous functions f:[0, 1] → [0, 1] endowed with the supremum norm. We prove that some properties shared by a residual set of continuous functions, e.g. the typical level set structure, and the existence of periodic points of order 3 hold a.e. with respect to the Wiener measure.

UR - http://www.scopus.com/inward/record.url?scp=84966246409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966246409&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1989-0961409-6

DO - 10.1090/S0002-9939-1989-0961409-6

M3 - Article

VL - 106

SP - 455

EP - 463

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -