On the Absolute Continuity of Distributions of Functionals of Random Processes

1983 ◽  
Vol 27 (3) ◽  
pp. 600-607 ◽  
Author(s):  
M. A. Lifshits
Keyword(s):  
Absolute Continuity ◽  
Random Processes ◽  
The Absolute

On the Absolute Continuity of Elliptic Measures

1986 ◽  
Vol 108 (5) ◽  
pp. 1119 ◽  
Author(s):  
Bjorn E. J. Dahlberg
Keyword(s):  
Absolute Continuity ◽  
The Absolute

Genetics, Epigenetics, and Talent

Sport ◽  
2016 ◽  
Author(s):  
Jay Schulkin
Keyword(s):  
Absolute Continuity ◽  
The Absolute

Looks at genes and their expression in athletic capability. There is no athletic gene; there is a general confluence of specific and general capabilities that converge on athletic expression. Such events reflect experience, culture and epigenetic expression; the absolute continuity of biology and culture; both a reflection of one another.

On the absolute continuity of distributions of occupation times

1998 ◽  
Vol 88 (1) ◽  
pp. 13-21
Author(s):  
Yu. A. Davydov ◽  
Sun Xian-Go
Keyword(s):  
Absolute Continuity ◽  
Occupation Times ◽  
The Absolute

scholarly journals Elliptic Measures and Square Function Estimates on 1-Sided Chord-Arc Domains

2022 ◽  
Vol 32 (3) ◽  
Author(s):  
Mingming Cao ◽  
José María Martell ◽  
Andrea Olivo
Keyword(s):  
Absolute Continuity ◽  
Square Function ◽  
Surface Measure ◽  
Antisymmetric Part ◽  
Null Solution ◽  
Almost Everywhere ◽  
Square Function Estimates ◽  
The Absolute ◽  
The Laplace Operator ◽  
Conical Square Function

AbstractIn nice environments, such as Lipschitz or chord-arc domains, it is well-known that the solvability of the Dirichlet problem for an elliptic operator in $$L^p$$ L p , for some finite p, is equivalent to the fact that the associated elliptic measure belongs to the Muckenhoupt class $$A_\infty $$ A ∞ . In turn, any of these conditions occurs if and only if the gradient of every bounded null solution satisfies a Carleson measure estimate. This has been recently extended to much rougher settings such as those of 1-sided chord-arc domains, that is, sets which are quantitatively open and connected with a boundary which is Ahlfors–David regular. In this paper, we work in the same environment and consider a qualitative analog of the latter equivalence showing that one can characterize the absolute continuity of the surface measure with respect to the elliptic measure in terms of the finiteness almost everywhere of the truncated conical square function for any bounded null solution. As a consequence of our main result particularized to the Laplace operator and some previous results, we show that the boundary of the domain is rectifiable if and only if the truncated conical square function is finite almost everywhere for any bounded harmonic function. In addition, we obtain that for two given elliptic operators $$L_1$$ L 1 and $$L_2$$ L 2 , the absolute continuity of the surface measure with respect to the elliptic measure of $$L_1$$ L 1 is equivalent to the same property for $$L_2$$ L 2 provided the disagreement of the coefficients satisfy some quadratic estimate in truncated cones for almost everywhere vertex. Finally, for the case on which $$L_2$$ L 2 is either the transpose of $$L_1$$ L 1 or its symmetric part we show the equivalence of the corresponding absolute continuity upon assuming that the antisymmetric part of the coefficients has some controlled oscillation in truncated cones for almost every vertex.

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