A problem with the Lebesgue-Stieltjes measure
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Let $f:mathbbR mapsto mathbbR$ be a nondecreasing function and let $lambda_f$ be the LebesgueâÂÂStieltjes measure generated by $f$. Prove that $lambda_f(x_0)=0$ if and only if $f$ is left-continuous at $x_0$.
measure-theory lebesgue-measure
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up vote
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Let $f:mathbbR mapsto mathbbR$ be a nondecreasing function and let $lambda_f$ be the LebesgueâÂÂStieltjes measure generated by $f$. Prove that $lambda_f(x_0)=0$ if and only if $f$ is left-continuous at $x_0$.
measure-theory lebesgue-measure
This is an immediate consequence of the definition of the Lebesgue-Stieltjes measure.
â MathOverview
Sep 10 at 21:17
Could you explain to me in what form? It is an exercise in my task.
â EuMJsus
Sep 11 at 2:02
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
Let $f:mathbbR mapsto mathbbR$ be a nondecreasing function and let $lambda_f$ be the LebesgueâÂÂStieltjes measure generated by $f$. Prove that $lambda_f(x_0)=0$ if and only if $f$ is left-continuous at $x_0$.
measure-theory lebesgue-measure
Let $f:mathbbR mapsto mathbbR$ be a nondecreasing function and let $lambda_f$ be the LebesgueâÂÂStieltjes measure generated by $f$. Prove that $lambda_f(x_0)=0$ if and only if $f$ is left-continuous at $x_0$.
measure-theory lebesgue-measure
measure-theory lebesgue-measure
asked Sep 10 at 21:03
EuMJsus
42
42
This is an immediate consequence of the definition of the Lebesgue-Stieltjes measure.
â MathOverview
Sep 10 at 21:17
Could you explain to me in what form? It is an exercise in my task.
â EuMJsus
Sep 11 at 2:02
add a comment |Â
This is an immediate consequence of the definition of the Lebesgue-Stieltjes measure.
â MathOverview
Sep 10 at 21:17
Could you explain to me in what form? It is an exercise in my task.
â EuMJsus
Sep 11 at 2:02
This is an immediate consequence of the definition of the Lebesgue-Stieltjes measure.
â MathOverview
Sep 10 at 21:17
This is an immediate consequence of the definition of the Lebesgue-Stieltjes measure.
â MathOverview
Sep 10 at 21:17
Could you explain to me in what form? It is an exercise in my task.
â EuMJsus
Sep 11 at 2:02
Could you explain to me in what form? It is an exercise in my task.
â EuMJsus
Sep 11 at 2:02
add a comment |Â
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This is an immediate consequence of the definition of the Lebesgue-Stieltjes measure.
â MathOverview
Sep 10 at 21:17
Could you explain to me in what form? It is an exercise in my task.
â EuMJsus
Sep 11 at 2:02