<s>
In	O
mathematics	O
,	O
specifically	O
in	O
order	O
theory	O
and	O
functional	B-Application
analysis	I-Application
,	O
an	O
abstract	B-Algorithm
L-space	I-Algorithm
,	O
an	O
AL-space	B-Algorithm
,	O
or	O
an	O
abstract	O
Lebesgue	O
space	O
is	O
a	O
Banach	O
lattice	O
whose	O
norm	O
is	O
additive	O
on	O
the	O
positive	O
cone	O
of	O
X	O
.	O
</s>
<s>
The	O
strong	O
dual	O
of	O
an	O
AM-space	B-Algorithm
with	O
unit	O
is	O
an	O
AL-space	B-Algorithm
.	O
</s>
<s>
Every	O
AL-space	B-Algorithm
X	O
is	O
an	O
order	B-Algorithm
complete	I-Algorithm
vector	B-Algorithm
lattice	I-Algorithm
of	O
minimal	B-Algorithm
type	I-Algorithm
;	O
</s>
<s>
however	O
,	O
the	O
order	B-Algorithm
dual	I-Algorithm
of	O
X	O
,	O
denoted	O
by	O
X+	O
,	O
is	O
not	O
of	O
minimal	B-Algorithm
type	I-Algorithm
unless	O
X	O
is	O
finite-dimensional	O
.	O
</s>
<s>
Each	O
order	O
interval	O
in	O
an	O
AL-space	B-Algorithm
is	O
weakly	O
compact	O
.	O
</s>
<s>
The	O
strong	O
dual	O
of	O
an	O
AL-space	B-Algorithm
is	O
an	O
AM-space	B-Algorithm
with	O
unit	O
.	O
</s>
<s>
The	O
continuous	O
dual	O
space	O
(	O
which	O
is	O
equal	O
to	O
X+	O
)	O
of	O
an	O
AL-space	B-Algorithm
X	O
is	O
a	O
Banach	O
lattice	O
that	O
can	O
be	O
identified	O
with	O
,	O
where	O
K	O
is	O
a	O
compact	O
extremally	O
disconnected	O
topological	O
space	O
;	O
</s>
