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Essay text:
Convergence in the Hausdor Metric 12
3.3. Examples 13
3.4. Remark 14
3.5. Parametrised Curves 14
4. Invariant Measures 15
4.1. Motivation 15
4.2. De nitions 16
4.3. The L metric 16
4.4. Existence and Uniqueness 16
4.5. Di erent Sets of Similitudes Generating the Same Set 17
5. Similitudes 18
5.1. Self-Similar Sets 18
5.2. Open Set Condition 18
5.3. Existence of Self Similar Sets. 19
5.4. Purely Unrecti able Sets. 21
5.5. Parameter Space 24
6. Integral Flat Chains 24
6.1. The F-metric. 24
6.2. The C-metric 25
6.3. Invariant Chains 26
References 27
1
2 JOHN E. HUTCHINSON
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