In mathematics, the Christ–Kiselev maximal inequality is a
maximal inequality for
filtrations, named for mathematicians
Michael Christ
Michael A. Christ is Director of Legislative Affairs for Connecticut Governor Dannel Malloy, as well as an attorney and former Democratic politician from East Hartford, Connecticut. After winning election in 1994 and until 2009, he served the ...
and
Alexander Kiselev.
[M. Christ, A. Kiselev, Maximal functions associated to filtrations. J. Funct. Anal. 179 (2001), no. 2, 409--425. ]
Continuous filtrations
A continuous filtration of
is a family of measurable sets
such that
#
,
, and
for all
(stratific)
#
(continuity)
For example,
with measure
that has no pure points and
:
is a continuous filtration.
Continuum version
Let