ABSTRACT
The rearrangement-invariant hull and kernel of a given noninvariant function class indicate how far this class is from being rearrangement-invariant. The hull of A is defined as the smallest invariant class containing A , while the kernel of A is the largest invariant class contained in A . The problem of finding the hull and kernel of a noninvariant function class has been studied in different settings by many mathematicians. This problem originates in the pioneering work of Hardy and Littlewood [9], [10]. They introduced the equimeasurability relation for measurable functions and solved the equimeasurable hull and kernel problem in special cases. However, Hardy and Littlewood did not use the hull and kernel terminology. The general hull and kernel problem was formulated by Cereteli (see [1]) in the case of an equivalence relation defined on a set. Cereteli initiated the systematic study of hulls and kernels of function classes. In [3], [4], [5], [6], [7] the reader can find more references to previous work on the hull and kernel problem.
