### Abstract

Extensions of the measurement theory literature regarding laws of exchange are obtained. It is shown that the theorems of R. D. Luce and A. A. J. Marley about combining conjoint measurement on a product A//1 multiplied by A//2 with extensive measurement on A//1 and A//2 still hold if extensive measurement on one or both of the components is replaced with qualitative probability measurement. The results in the case where one components is replaced with qualitative probability measurement. The results in the case where one component has qualitative probability measurement and one has extensive measurement are applied to give an extension of the Savage axioms of statistical decision theory to the case of additive utility functions. They are also applied to the foundations of integration and to the measurement of the community noise exposure level. The case of qualitative probability measurement on both components is applied to time preference. 28 refs.

Original language | English (US) |
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Pages (from-to) | 260-284 |

Number of pages | 25 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 26 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1974 |

### All Science Journal Classification (ASJC) codes

- Applied Mathematics