Abstract :
The author proves a new theoretical property for the family of rearrangements
R f. of a given measurable function f. Given a finite number of equimeasurable
functions f1, . . . , fngR f., it is possible to construct a family of equimeasurable
functions h . ;R f.which interpolates the functions f , . . . , f in a convex- l lgw0, 1x 1 n
like way. However, as an application, this interpolation result yields a compact
fixed point property
