Continuous dependence on parameters of certain self-affine measures, and their singularity

Daoxin Ding

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 2, page 495-508
  • ISSN: 0011-4642

Abstract

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In this paper, we first prove that the self-affine sets depend continuously on the expanding matrix and the digit set, and the corresponding self-affine measures with respect to the probability weight behave in much the same way. Moreover, we obtain some sufficient conditions for certain self-affine measures to be singular.

How to cite

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Ding, Daoxin. "Continuous dependence on parameters of certain self-affine measures, and their singularity." Czechoslovak Mathematical Journal 61.2 (2011): 495-508. <http://eudml.org/doc/196983>.

@article{Ding2011,
abstract = {In this paper, we first prove that the self-affine sets depend continuously on the expanding matrix and the digit set, and the corresponding self-affine measures with respect to the probability weight behave in much the same way. Moreover, we obtain some sufficient conditions for certain self-affine measures to be singular.},
author = {Ding, Daoxin},
journal = {Czechoslovak Mathematical Journal},
keywords = {iterated function system; self-affine set; self-affine measure; singularity; iterated function system; self-affine set; self-affine measure; singularity},
language = {eng},
number = {2},
pages = {495-508},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Continuous dependence on parameters of certain self-affine measures, and their singularity},
url = {http://eudml.org/doc/196983},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Ding, Daoxin
TI - Continuous dependence on parameters of certain self-affine measures, and their singularity
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 495
EP - 508
AB - In this paper, we first prove that the self-affine sets depend continuously on the expanding matrix and the digit set, and the corresponding self-affine measures with respect to the probability weight behave in much the same way. Moreover, we obtain some sufficient conditions for certain self-affine measures to be singular.
LA - eng
KW - iterated function system; self-affine set; self-affine measure; singularity; iterated function system; self-affine set; self-affine measure; singularity
UR - http://eudml.org/doc/196983
ER -

References

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