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Open-Invariant Measures and the Covering Number of Sets

✍ Scribed by Hermann Haase

Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
598 KB
Volume
134
Category
Article
ISSN
0025-584X

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✦ Synopsis

A reault of J. MYCIELSIZI ssp that on every metric space (X, e) with a non-empty compact thick set C X there exists a repbr open-invsriant BOREL measure p with p(C) = 1. p is mlled open-invariant if p(A) = p(B) for open isometric sets A, 3 X. We relste this result to the notion of a Hrrwm~-S~~omms~ measure and give s new independent existence proof for euch an open-invariant measure p on s compact metric apace (X, e). This proof worka by induction, the well-known metric outer maonstruction of C ~~D O R Y : H A W S D O R S S and s new property of the covering number N(X, q) of X.

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