Previous:
A.1 Norms
Up:
A. Mathematical Preliminaries
Next:
A.3 Inequalities
A.
2
Means
Definition A..
4
(Weighted Mean)
is called a vector of weights if
for all
. For
,
, and
a vector of weights we define the weighted
-mean of
as follows:
:
,
:
,
and one
:
.
In the case where all
are equal we also write shorter
.
Theorem A..
5
(Inequality of the Means) If
then
unless the
are all equal, or
and one
is zero.
Remark.
Many more properties of means can be found in [
43
].
Remark.
For
, obviously
.
Previous:
A.1 Norms
Up:
A. Mathematical Preliminaries
Next:
A.3 Inequalities
Clemens Heitzinger 2003-05-08