## Abstract

The concept of composite differentiation was introduced by O'Malley and Weil to generalize approximate differentiation. The concept of con- tinuous path systems was introduced by us. This paper combines these concepts to introduce the notion of composite continuous path systems into differentiation theory. It is shown that a number of results that hold for composite differentiation and for continuous path differentiation also hold for composite continuous path differentiation. In particular, a com- posite continuous path derivative of a continuous function is a Baire class one function on some dense open set, and extreme composite continuous path derivatives of a continuous function are Baire class two functions. It is also shown that extreme composite continuous path derivatives of a Borel measurable function are Lebesgue measurable. Finally, for each composite continuous path system E, continuous functions typically do not have E-derived numbers with E-index less than one.

Original language | English (US) |
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Pages (from-to) | 31-42 |

Number of pages | 12 |

Journal | Real Analysis Exchange |

Volume | 35 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2010 |

## All Science Journal Classification (ASJC) codes

- Analysis
- Geometry and Topology