The possible almost sure large Φ-dimensions of random Moran measures are fully characterized, revealing a typical gap between set dimension and attainable measure dimensions when weights are scale-independent.
Petrov,Limit theorems of probability theory: Sequences of independent random variables, Oxford Studies in Probability vol 4, Oxford
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The attainable almost sure large dimensions
The possible almost sure large Φ-dimensions of random Moran measures are fully characterized, revealing a typical gap between set dimension and attainable measure dimensions when weights are scale-independent.