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Topic: Science
Number of pages / Number of words: 49 / 13512
Essay's paper body

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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