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- Mar 15th 2009, 10:38 PM #1

- Joined
- Oct 2008
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- 156

## Refinements

**Theorem.**Let , and let be bounded on . If is a partition of and is a refinement of , then .

**Proof.**By definition, and . In the refinement , we are "throwing" extra points in . If we sample exactly the same points from each partition, there will be equality. However, if we sample different points, and will have larger values for .

Is this correct?