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Partition of an infinite-dimensional interval

  1. Apr 30, 2007 #1

    tpm

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    Is ther any form by bisection or simiar to obtain a partition for an infinite-dimensional interval (aka functional space)?? i believe you could obtain a partition for every interval 'centered' at a certain function as:

    [tex] X(t), X(t)+\delta (t-t`), X(t)+2\delta (t-t`), X(t)+\delta (t-t`), ..... [/tex]

    where X(t) is the center of the partition in the sense that the mean value of..

    [tex] \sum_{i=1}^{N} \frac{ Y_{i} (t)}{N}=X(t) [/tex]

    where the Y_i (t) are the 'elements' of the partition...
     
  2. jcsd
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