Let be any two partitions of . Let . Show that is also a partition of and it is a
refinement of both . (It is called the common refinement of ). Further show that
Let be a sequence of partitions of . Define
Show that is a sequence of refinement partitions of .
, compute 
: 
be any two partitions of 
. Let 
. Show that 
is also a partition of 
and it is a 
. (It is called the 
). Further show that 
be a sequence of partitions of 
. Define 
is a sequence of refinement partitions of 
. 
