Let be a function in an Orlicz space and be the set of all the best -approximants to given a lattice Weak type inequalities are proved for the maximal operator where is any selection of functions in and is an increasing sequence of -lattices. Strong inequalities are proved in an abstract set up which can be used for an operator as .
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be a function in an Orlicz space 
and 
be the set of all the best 
-approximants to 
given a 
lattice 
Weak type inequalities are proved for the maximal operator 
where 
is any selection of functions in 
and 
is an increasing sequence of 
-lattices. Strong inequalities are proved in an abstract set up which can be used for an operator as 
.
