# Partition of an infinite-dimensional interval

1. Apr 30, 2007

### tpm

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:

$$X(t), X(t)+\delta (t-t), X(t)+2\delta (t-t), X(t)+\delta (t-t`), .....$$

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

$$\sum_{i=1}^{N} \frac{ Y_{i} (t)}{N}=X(t)$$

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