Mixing
Hahn-Komolgorov Extension Theorem
$begingroup$
The following seems like a very easy question to answer, but I am not able to answer it. Here's the question:
Let $mathcal{A}$ be the
collection of all subsets in $mathbb{R}$ that can be expressed as finite unions of
half-open intervals $[a, b)$. Let $µ_{0} : A longrightarrow [ 0, + infty ]$ be the function such
that $µ_{0}(E) = infty$ for non-empty $E$ and $µ_{0}(emptyset) = 0$. Show that the Hahn-Komologorv extension $mu$, restricted to Borel measurable sets, assigns infinite measure to all Borel measurable sets.
I'm stuck how to go about solving this problem. Any suggestions would be welcome.
measure-theory
asked Jan 24 at 2:58
user82261user82261
27017
$endgroup$
add a comment |
$begingroup$
The following seems like a very easy question to answer, but I am not able to answer it. Here's the question:
Let $mathcal{A}$ be the
collection of all subsets in $mathbb{R}$ that can be expressed as finite unions of
half-open intervals $[a, b)$. Let $µ_{0} : A longrightarrow [ 0, + infty ]$ be the function such
that $µ_{0}(E) = infty$ for non-empty $E$ and $µ_{0}(emptyset) = 0$. Show that the Hahn-Komologorv extension $mu$, restricted to Borel measurable sets, assigns infinite measure to all Borel measurable sets.
I'm stuck how to go about solving this problem. Any suggestions would be welcome.
measure-theory
asked Jan 24 at 2:58
user82261user82261
27017
$endgroup$
add a comment |
$begingroup$
The following seems like a very easy question to answer, but I am not able to answer it. Here's the question:
Let $mathcal{A}$ be the
collection of all subsets in $mathbb{R}$ that can be expressed as finite unions of
half-open intervals $[a, b)$. Let $µ_{0} : A longrightarrow [ 0, + infty ]$ be the function such
that $µ_{0}(E) = infty$ for non-empty $E$ and $µ_{0}(emptyset) = 0$. Show that the Hahn-Komologorv extension $mu$, restricted to Borel measurable sets, assigns infinite measure to all Borel measurable sets.
I'm stuck how to go about solving this problem. Any suggestions would be welcome.
measure-theory
asked Jan 24 at 2:58
user82261user82261
27017
$endgroup$
The following seems like a very easy question to answer, but I am not able to answer it. Here's the question:
Let $mathcal{A}$ be the
collection of all subsets in $mathbb{R}$ that can be expressed as finite unions of
half-open intervals $[a, b)$. Let $µ_{0} : A longrightarrow [ 0, + infty ]$ be the function such
that $µ_{0}(E) = infty$ for non-empty $E$ and $µ_{0}(emptyset) = 0$. Show that the Hahn-Komologorv extension $mu$, restricted to Borel measurable sets, assigns infinite measure to all Borel measurable sets.
I'm stuck how to go about solving this problem. Any suggestions would be welcome.
measure-theory
measure-theory
asked Jan 24 at 2:58
user82261user82261
27017
asked Jan 24 at 2:58
user82261user82261
27017
asked Jan 24 at 2:58
user82261user82261
27017
asked Jan 24 at 2:58
user82261user82261
27017
asked Jan 24 at 2:58
user82261user82261
27017
27017
add a comment |
add a comment |
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