Note that the continuous dual space
(
our website
C
c
0
look at more info
(
U
)
)
b
{\displaystyle (C_{c}^{0}(U))’_{b}}
can be identified as the space of Radon measures, where there is a one-to-one correspondence between the continuous linear functionals
T
(
C
c
0
(
U
)
)
b
{\displaystyle T\in (C_{c}^{0}(U))’_{b}}
and integral with respect to a Radon measure; that is,
Through the injection
t
In
:
(
C
c
0
(
U
)
)
b
D
(
U
)
,
{\displaystyle {}^{t}\operatorname {In} :(C_{c}^{0}(U))’_{b}\to {\mathcal {D}}'(U),}
every Radon measure becomes a distribution on U. .