scholarly journals Absolute Continuity of Bernoulli Convolutions, A Simple Proof

1996 ◽  
Vol 3 (2) ◽  
pp. 231-239 ◽  
Author(s):  
Yuval Peres ◽  
Boris Solomyak
Keyword(s):  
Simple Proof ◽  
Absolute Continuity ◽  
Bernoulli Convolutions

scholarly journals Almost sure absolute continuity of Bernoulli convolutions

2010 ◽  
Vol 46 (3) ◽  
pp. 888-893 ◽  
Author(s):  
Michael Björklund ◽  
Daniel Schnellmann
Keyword(s):  
Absolute Continuity ◽  
Bernoulli Convolutions

scholarly journals Absolute continuity of complex Bernoulli convolutions

2016 ◽  
Vol 161 (3) ◽  
pp. 435-453 ◽  
Author(s):  
PABLO SHMERKIN ◽  
BORIS SOLOMYAK
Keyword(s):  
Hausdorff Dimension ◽  
Complex Plane ◽  
Absolute Continuity ◽  
Exceptional Set ◽  
Parameter Region ◽  
Absolutely Continuous ◽  
Bernoulli Convolutions ◽  
Supercritical Parameter ◽  
Self Similar

AbstractWe prove that complex Bernoulli convolutions are absolutely continuous in the supercritical parameter region, outside of an exceptional set of parameters of zero Hausdorff dimension. Similar results are also obtained in the biased case, and for other parametrised families of self-similar sets and measures in the complex plane, extending earlier results.

On the equivalence of the properties of quasi-translation invariance and absolute continuity of measures on a locally compact abelian group

1987 ◽  
Vol 101 (2) ◽  
pp. 279-281
Author(s):  
Denis Bell
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Simple Proof ◽  
Compact Abelian Group ◽  
Absolute Continuity ◽  
Locally Compact Abelian Group ◽  
Translation Invariance ◽  
Positive Density ◽  
Locally Compact ◽  
Translation Invariant

AbstractWe give a simple proof that a measure on a locally compact abelian group G is quasi-translation invariant with continuous translation densities if and only if it is equivalent to Haar measure on G and has a continuous positive density.

scholarly journals A simple proof of Andrews’s 5 F 4 evaluation

2013 ◽  
Vol 36 (1-2) ◽  
pp. 165-170 ◽  
Author(s):  
Ira M. Gessel
Keyword(s):  
Simple Proof
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