 

Norbert Hungerbühler
A Refinement of Ball's Theorem on Young Measures


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


Abstract
For a sequence u_{j}:Ω⊂ R^{n}→ R^{m}
generating the Young measure ν_{x}, x∈Ω, Ball's Theorem
asserts that a tightness condition preventing mass in the target from escaping
to infinity implies that ν_{x} is a probability measure and that
f(u_{k})⇀<ν_{x},f> in L^{1} 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 ∥ν_{x}∥=1, and the convergence
conclusion, are equivalent. We give some simple applications of this
observation.


Author information
Departement Mathematik, ETHZentrum, CH8092 Zürich (Switzerland)
buhler@math.ethz.ch
http://www.math.ethz.ch/~buhler/noebi.html

