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| Topic: |
Science
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| Number of pages / Number of words: |
49 / 13512 |
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Then there exists a unique closed bounded
set K such that K = SN
i=1 SiK. Furthermore, K is compact and is the closure of
the set of xed points si1:::ip of nite compositions Si1 Sip of members of S.
For arbitrary A X let S(A) = SN
i=1 SiA, Sp(A) = S(Sp??1(A)). Then for
closed bounded A, Sp(A) ! K in the Hausdor metric (2...
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Then for
closed bounded A, Sp(A) ! K in the Hausdor metric (2.4).
The compact set K in (1) is denoted jSj. jSj supports various measures in a
natural way. We have the following from 4.4.
(2) In addition to the hypotheses of (1), suppose 1; : : : ; N 2 (0; 1) and
PN
i=1 i = 1. Then there exists a unique Borel regular measure of total mass 1
such that = PN
i=1 iSi#()...
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