On Isbell's density theorem for bitopological pointfree spaces I

2020 ◽  
Vol 273 ◽  
pp. 106962
Author(s):  
M. Andrew Moshier ◽  
Imanol Mozo Carollo ◽  
Joanne Walters-Wayland
Keyword(s):  
Density Theorem

A new proof for the residual set dimension of the apollonian packing

1984 ◽  
Vol 96 (3) ◽  
pp. 413-423 ◽  
Author(s):  
Claude Tricot
Keyword(s):  
Hausdorff Dimension ◽  
Density Theorem ◽  
Residual Set ◽  
Curvilinear Triangle

AbstractLet (Dn) be the apollonian packing of a curvilinear triangle T, ρn the radius of Dn, E = T—U Dn the residual set, dim (E) its Hausdorff dimension. In this paper we give a new proof of the equality dim proved by Boyd [2]. Our technique is to construct a sequence of regular triangles covering E, and suitable measures μkcarried by E which allow us to apply a density theorem.

scholarly journals A Converse of Artin′s Density Theorem: The Case of Cubic Fields

1993 ◽  
Vol 45 (1) ◽  
pp. 28-44 ◽  
Author(s):  
I. Delcorso ◽  
R. Dvornicich
Keyword(s):  
Density Theorem ◽  
Cubic Fields

A renewal density theorem in the multi-dimensional case

1967 ◽  
Vol 4 (1) ◽  
pp. 62-76 ◽  
Author(s):  
Charles J. Mode
Keyword(s):  
Density Function ◽  
Covariance Matrix ◽  
Branching Processes ◽  
Random Variable ◽  
Density Theorem ◽  
Positive Definite ◽  
Dimensional Case ◽  
Age Dependent ◽  
Image Position ◽  
Mean Vector

SummaryIn this note a renewal density theorem in the multi-dimensional case is formulated and proved. Let f(x) be the density function of a p-dimensional random variable with positive mean vector μ and positive-definite covariance matrix Σ, let hn(x) be the n-fold convolution of f(x) with itself, and set Then for arbitrary choice of integers k1, …, kp–1 distinct or not in the set (1, 2, …, p), it is shown that under certain conditions as all elements in the vector x = (x1, …, xp) become large. In the above expression μ‵ is interpreted as a row vector and μ a column vector. An application to the theory of a class of age-dependent branching processes is also presented.

A Short Proof of Lebesgue's Density Theorem

2002 ◽  
Vol 109 (2) ◽  
pp. 194-196 ◽  
Author(s):  
Claude-Alain Faure
Keyword(s):  
Short Proof ◽  
Density Theorem

scholarly journals An explicit Chebotarev density theorem under GRH

2019 ◽  
Vol 200 ◽  
pp. 441-485 ◽  
Author(s):  
Loïc Grenié ◽  
Giuseppe Molteni
Keyword(s):  
Density Theorem ◽  
Chebotarev Density Theorem

scholarly journals Chebotarëv and his density theorem

1996 ◽  
Vol 18 (2) ◽  
pp. 26-37 ◽  
Author(s):  
P. Stevenhagen ◽  
H. W. Lenstra
Keyword(s):  
Density Theorem
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