### Resumen

We show that a single application of the non-computable operator EC, which transforms enumerations of sets (in ℕ) to their characteristic functions, suffices to compute the Radon-Nikodym derivative dμ/dλ of a finite measure μ, which is absolutely continuous w.r.t. the σ-finite measure λ. We also give a condition on the two measures (in terms of computability of the norm of a certain linear operator involving the two measures) which is sufficient to compute the derivative.

Idioma original | English |
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Título de la publicación alojada | Models of Computation in Context - 7th Conference on Computability in Europe, CiE 2011, Proceedings |

Páginas | 132-141 |

Número de páginas | 10 |

Volumen | 6735 LNCS |

DOI | |

Estado | Published - 2011 |

Evento | 7th Conference on Computability in Europe, CiE 2011 - Sofia, Bulgaria Duración: 27 jun 2011 → 2 jul 2011 |

### Serie de la publicación

Nombre | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volumen | 6735 LNCS |

ISSN (versión impresa) | 03029743 |

ISSN (versión digital) | 16113349 |

### Other

Other | 7th Conference on Computability in Europe, CiE 2011 |
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País | Bulgaria |

Ciudad | Sofia |

Período | 27/06/11 → 2/07/11 |

### Huella dactilar

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Citar esto

*Models of Computation in Context - 7th Conference on Computability in Europe, CiE 2011, Proceedings*(Vol. 6735 LNCS, pp. 132-141). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6735 LNCS). https://doi.org/10.1007/978-3-642-21875-0_14

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*Models of Computation in Context - 7th Conference on Computability in Europe, CiE 2011, Proceedings.*vol. 6735 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6735 LNCS, pp. 132-141, 7th Conference on Computability in Europe, CiE 2011, Sofia, Bulgaria, 27/06/11. https://doi.org/10.1007/978-3-642-21875-0_14

**Computability of the Radon-Nikodym derivative.** / Hoyrup, Mathieu; Rojas, Cristóbal; Weihrauch, Klaus.

Resultado de la investigación: Conference contribution

TY - GEN

T1 - Computability of the Radon-Nikodym derivative

AU - Hoyrup, Mathieu

AU - Rojas, Cristóbal

AU - Weihrauch, Klaus

PY - 2011

Y1 - 2011

N2 - We show that a single application of the non-computable operator EC, which transforms enumerations of sets (in ℕ) to their characteristic functions, suffices to compute the Radon-Nikodym derivative dμ/dλ of a finite measure μ, which is absolutely continuous w.r.t. the σ-finite measure λ. We also give a condition on the two measures (in terms of computability of the norm of a certain linear operator involving the two measures) which is sufficient to compute the derivative.

AB - We show that a single application of the non-computable operator EC, which transforms enumerations of sets (in ℕ) to their characteristic functions, suffices to compute the Radon-Nikodym derivative dμ/dλ of a finite measure μ, which is absolutely continuous w.r.t. the σ-finite measure λ. We also give a condition on the two measures (in terms of computability of the norm of a certain linear operator involving the two measures) which is sufficient to compute the derivative.

UR - http://www.scopus.com/inward/record.url?scp=80053025936&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-21875-0_14

DO - 10.1007/978-3-642-21875-0_14

M3 - Conference contribution

AN - SCOPUS:80053025936

SN - 9783642218743

VL - 6735 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 132

EP - 141

BT - Models of Computation in Context - 7th Conference on Computability in Europe, CiE 2011, Proceedings

ER -