Open AccessNorms on earthquake measures and Zygmund functions
Author(s) -
Jun Hu
Publication year - 2004
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-04-07545-8
Subject(s) - bounded function , infinitesimal , mathematics , bounded deformation , norm (philosophy) , function (biology) , measure (data warehouse) , pure mathematics , mathematical analysis , discrete mathematics , uniform boundedness , computer science , database , evolutionary biology , political science , law , biology
The infinitesimal earthquake theorem gives a one-to-one correspondence between Thurston bounded earthquake measures and normalized Zygmund bounded functions. In this paper, we provide an intrinsic proof of a theorem given in an earlier paper by the author; that is, we show that the cross-ratio norm of a Zygmund bounded function is equivalent to the Thurston norm of the earthquake measure in the correspondence.