Theorem
examples of r.v.s produced by measurable maps
component sum:
g
(
x
1
,
…
,
x
n
)
=
∑
i
=
1
n
x
i
g(x_1 , \dots , x_n ) = \sum_{i=1}^{n} x_i
component average:
g
(
x
1
,
…
,
x
n
)
=
1
n
∑
i
=
1
n
x
i
g(x_1 , \dots , x_n ) = \frac{1}{n}\sum_{i=1}^{n} x_i
component extreme:
g
(
x
1
,
…
,
x
n
)
=
⋁
i
=
1
n
x
i
g(x_1 , \dots , x_n ) = \bigvee_{i=1}^{n} x_i
component product:
g
(
x
1
,
…
,
x
n
)
=
∏
i
=
1
n
x
i
g(x_1 , \dots , x_n ) = \prod_{i=1}^{n} x_i
component sum of squares:
g
(
x
1
,
…
,
x
n
)
=
∑
i
=
1
n
x
i
2
g(x_1 , \dots , x_n ) = \sum_{i=1}^{n} x_i^2
projection of component
i
i
:
g
(
x
1
,
…
,
x
n
)
=
x
i
g(x_1 , \dots , x_n ) = x_i