The Lipschitz extension problem asks whether a Lipschitz function 
on a subset 
of a metric space 
extends to 
with controlled Lipschitz
constant. A uniform extension factor 
requires 
and 
for every 
and 
.
For a nonempty 
and a real-valued 
-Lipschitz function,
McShane's extension (McShane 1934) is
 |
It has Lipschitz constant at most 
and agrees with 
on 
. Vector-valued targets can require a larger factor or fail
to have a uniform factor.
Ball's problem for the target 
asks for a universal extension factor when 
is a real Hilbert space and
is the Banach space of absolutely summable real sequences
with 
(Ball 1992, Mendel and Naor 2013).
