TY - JOUR
T1 - Points of infinite derivative of Cantor functions
AU - Li, Wenxia
PY - 2007
Y1 - 2007
N2 - We consider self-similar Borel probability measures μ on a self-similar set E with strong separation property. We prove that for any such measure μ the derivative of its distribution function F(x) is infinite for μ-a.e. x ∈ E, and so the set of points at which F(x) has no derivative, finite or infinite is of μ-zero.
AB - We consider self-similar Borel probability measures μ on a self-similar set E with strong separation property. We prove that for any such measure μ the derivative of its distribution function F(x) is infinite for μ-a.e. x ∈ E, and so the set of points at which F(x) has no derivative, finite or infinite is of μ-zero.
KW - Cantor functions
KW - Non-differentiability
KW - Self-similar measures
KW - Self-similar sets
UR - https://www.scopus.com/pages/publications/72549119849
U2 - 10.14321/realanalexch.32.1.0087
DO - 10.14321/realanalexch.32.1.0087
M3 - 文章
AN - SCOPUS:72549119849
SN - 0147-1937
VL - 32
SP - 87
EP - 96
JO - Real Analysis Exchange
JF - Real Analysis Exchange
IS - 1
ER -