New York Journal of Mathematics
Volume 3 (1997) 48-53


Norbert Hungerbühler

A Refinement of Ball's Theorem on Young Measures

Published: May 2, 1997
Keywords: Young measures
Subject: 46E27, 28A33, 28A20

For a sequence uj:Ω⊂ RnRm generating the Young measure νx, x∈Ω, Ball's Theorem asserts that a tightness condition preventing mass in the target from escaping to infinity implies that νx is a probability measure and that f(uk)⇀<νx,f> in L1 provided the sequence is equiintegrable. Here we show that Ball's tightness condition is necessary for the conclusions to hold and that in fact all three, the tightness condition, the assertion ∥νx∥=1, and the convergence conclusion, are equivalent. We give some simple applications of this observation.

Author information

Departement Mathematik, ETH-Zentrum, CH-8092 Zürich (Switzerland)