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Christ–Kiselev maximal inequality : ウィキペディア英語版
Christ–Kiselev maximal inequality

In mathematics, the Christ–Kiselev maximal inequality is a maximal inequality for filtrations, named for mathematicians Michael Christ and Alexander Kiselev.〔M. Christ, A. Kiselev, Maximal functions associated to filtrations. J. Funct. Anal. 179 (2001), no. 2, 409--425. http://www.math.wisc.edu/~kiselev/maxim.pdf〕
==Continuous fibrations==
A continuous fibration of (M,\mu) is a family of measurable sets \_}A_\alpha=\emptyset, and \mu(A_\beta\setminus A_\alpha)<\infty for all \beta>\alpha (stratific)
# \lim_\mu(A_\setminus A_\alpha)=\lim_\mu(A_\alpha\setminus A_)=0 (continuity)
For example, \mathbb=M with measure \mu that has no pure points and
: A_\alpha:=\begin\,&\alpha>0, \\ \emptyset,&\alpha\le0. \end
is a continuous fibration.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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