# independence of valuations

Let $|\cdot {|}_{1}$, …, $|\cdot {|}_{n}$ be non-trivial (i.e., they all have also other values than 0 and 1) and pairwise non-equivalent valuations of a field $K$, all with values real numbers. If ${a}_{1}$, …, ${a}_{n}$ are some elements of this field and $\epsilon $ is an arbitrary positive number, then there exists in $K$ an element $y$ which satisfies the conditions

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Title | independence of valuations |
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Canonical name | IndependenceOfValuations |

Date of creation | 2013-03-22 14:11:44 |

Last modified on | 2013-03-22 14:11:44 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 22 |

Author | pahio (2872) |

Entry type | Theorem |

Classification | msc 11R99 |

Synonym | approximation theorem |

Related topic | TrivialValuation |

Related topic | EquivalentValuations |

Related topic | WeakApproximationTheorem |