TY - JOUR
T1 - Non-differentiability points of Cantor functions
AU - Li, Wenxia
PY - 2007
Y1 - 2007
N2 - Let the Cantor set C in ℝ be defined by C = Uj=0 r hj (C) disjoint union, where the hj's are similitude mappings with ratios 0 < aj < 1. Let μ be the self-similar Borel probability measure on C corresponding to the probability vector (p0, P1,...., Pr). Let 5 be the set of points at which the probability distribution function F(x) of μ has no derivative, finite or infinite. For the case where pi > ai we determine the packing and box dimensions of S and give an approach to calculate the Hausdorff dimension of S.
AB - Let the Cantor set C in ℝ be defined by C = Uj=0 r hj (C) disjoint union, where the hj's are similitude mappings with ratios 0 < aj < 1. Let μ be the self-similar Borel probability measure on C corresponding to the probability vector (p0, P1,...., Pr). Let 5 be the set of points at which the probability distribution function F(x) of μ has no derivative, finite or infinite. For the case where pi > ai we determine the packing and box dimensions of S and give an approach to calculate the Hausdorff dimension of S.
KW - Cantor function
KW - Hausdorff dimension
KW - Non-differentiability
KW - Packing dimension
UR - https://www.scopus.com/pages/publications/33846474753
U2 - 10.1002/mana.200410470
DO - 10.1002/mana.200410470
M3 - 文章
AN - SCOPUS:33846474753
SN - 0025-584X
VL - 280
SP - 140
EP - 151
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
IS - 1-2
ER -