<s>
The	O
Radon	B-Algorithm
–	I-Algorithm
Riesz	I-Algorithm
property	I-Algorithm
is	O
a	O
mathematical	O
property	O
for	O
normed	O
spaces	O
that	O
helps	O
ensure	O
convergence	B-Algorithm
in	O
norm	O
.	O
</s>
<s>
Given	O
two	O
assumptions	O
(	O
essentially	O
weak	O
convergence	B-Algorithm
and	O
continuity	O
of	O
norm	O
)	O
,	O
we	O
would	O
like	O
to	O
ensure	O
convergence	B-Algorithm
in	O
the	O
norm	O
topology	O
.	O
</s>
<s>
We	O
say	O
that	O
X	O
has	O
the	O
Radon	B-Algorithm
–	I-Algorithm
Riesz	I-Algorithm
property	I-Algorithm
(	O
or	O
that	O
X	O
is	O
a	O
Radon	O
–	O
Riesz	O
space	O
)	O
if	O
whenever	O
is	O
a	O
sequence	O
in	O
the	O
space	O
and	O
is	O
a	O
member	O
of	O
X	O
such	O
that	O
converges	O
weakly	O
to	O
and	O
,	O
then	O
converges	O
to	O
in	O
norm	O
;	O
that	O
is	O
,	O
.	O
</s>
<s>
Although	O
it	O
would	O
appear	O
that	O
Johann	O
Radon	O
was	O
one	O
of	O
the	O
first	O
to	O
make	O
significant	O
use	O
of	O
this	O
property	O
in	O
1913	O
,	O
M	O
.	O
I	O
.	O
Kadets	O
and	O
V	O
.	O
L	O
.	O
Klee	O
also	O
used	O
versions	O
of	O
the	O
Radon	B-Algorithm
–	I-Algorithm
Riesz	I-Algorithm
property	I-Algorithm
to	O
make	O
advancements	O
in	O
Banach	O
space	O
theory	O
in	O
the	O
late	O
1920s	O
.	O
</s>
<s>
It	O
is	O
common	O
for	O
the	O
Radon	B-Algorithm
–	I-Algorithm
Riesz	I-Algorithm
property	I-Algorithm
to	O
also	O
be	O
referred	O
to	O
as	O
the	O
Kadets	O
–	O
Klee	O
property	O
or	O
property	O
(	O
H	O
)	O
.	O
</s>
<s>
This	O
list	O
was	O
given	O
by	O
K	O
.	O
Fan	O
and	O
I	O
.	O
Glicksberg	O
(	O
Observe	O
that	O
the	O
definition	O
of	O
(	O
H	O
)	O
given	O
by	O
Fan	O
and	O
Glicksberg	O
includes	O
additionally	O
the	O
rotundity	O
of	O
the	O
norm	O
,	O
so	O
it	O
does	O
not	O
coincide	O
with	O
the	O
Radon-Riesz	B-Algorithm
property	I-Algorithm
itself	O
)	O
.	O
</s>
<s>
See	O
Section	O
3.7	O
of	O
Haim	O
Brezis	O
 '	O
Functional	B-Application
analysis	I-Application
.	O
</s>
