Analysis 3/Gemischte Satzabfrage/8/Aufgabe/Lösung
Es seien
n
{\displaystyle {}n}
σ
{\displaystyle {}\sigma }
endliche
Maßräume
(
M
1
,
A
1
,
μ
1
)
,
…
,
(
M
n
,
A
n
,
μ
n
)
{\displaystyle {}(M_{1},{\mathcal {A}}_{1},\mu _{1}),\ldots ,(M_{n},{\mathcal {A}}_{n},\mu _{n})}
σ
{\displaystyle {}\sigma }
μ
{\displaystyle {}\mu }
Produkt -
σ
{\displaystyle {}\sigma }
Algebra
A
1
⊗
⋯
⊗
A
n
{\displaystyle {}{\mathcal {A}}_{1}\otimes _{}\cdots \otimes _{}{\mathcal {A}}_{n}}
μ
(
T
1
×
⋯
×
T
n
)
=
μ
1
(
T
1
)
⋯
μ
n
(
T
n
)
{\displaystyle {}\mu (T_{1}\times \cdots \times T_{n})=\mu _{1}(T_{1}){\cdots }\mu _{n}(T_{n})\,}
/Fakt /Fakt
