Dtjytyk

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-1

$begingroup$

I'm having troubles understanding a statement in paper.
Basicly we have a function $u$ for which we know $0$ is a Lebesgue point. Moreover, we know that $u(0) > v$. Now, define the function
$$
chi(u,v)=
begin{cases}
1 & {rm if} 0 < v leq u, \
0 & otherwise,
end{cases}
$$
In particular we see that: $chi(u(0),v) = 1$. The claim is that $0$ is a Lebesgue point for $chi(u(cdot), v)$ with value $1$.

I tried to use the definition, but I can't see why this should be true (although I can imagine why intuitively).

Feel free to ask any clarification! Thank you very much!

analysis measure-theory lebesgue-measure

share|cite|improve this question

asked 15 hours ago

Lorenzo LiveraniLorenzo Liverani

243

$endgroup$

add a comment | 

-1

$begingroup$

I'm having troubles understanding a statement in paper.
Basicly we have a function $u$ for which we know $0$ is a Lebesgue point. Moreover, we know that $u(0) > v$. Now, define the function
$$
chi(u,v)=
begin{cases}
1 & {rm if} 0 < v leq u, \
0 & otherwise,
end{cases}
$$
In particular we see that: $chi(u(0),v) = 1$. The claim is that $0$ is a Lebesgue point for $chi(u(cdot), v)$ with value $1$.

I tried to use the definition, but I can't see why this should be true (although I can imagine why intuitively).

Feel free to ask any clarification! Thank you very much!

analysis measure-theory lebesgue-measure

share|cite|improve this question

asked 15 hours ago

Lorenzo LiveraniLorenzo Liverani

243

$endgroup$

add a comment | 

$begingroup$

I'm having troubles understanding a statement in paper.
Basicly we have a function $u$ for which we know $0$ is a Lebesgue point. Moreover, we know that $u(0) > v$. Now, define the function
$$
chi(u,v)=
begin{cases}
1 & {rm if} 0 < v leq u, \
0 & otherwise,
end{cases}
$$
In particular we see that: $chi(u(0),v) = 1$. The claim is that $0$ is a Lebesgue point for $chi(u(cdot), v)$ with value $1$.

I tried to use the definition, but I can't see why this should be true (although I can imagine why intuitively).

Feel free to ask any clarification! Thank you very much!

analysis measure-theory lebesgue-measure

share|cite|improve this question

asked 15 hours ago

Lorenzo LiveraniLorenzo Liverani

243

$endgroup$

share|cite|improve this question

asked 15 hours ago

Lorenzo LiveraniLorenzo Liverani

243

share|cite|improve this question

asked 15 hours ago

Lorenzo LiveraniLorenzo Liverani

243

asked 15 hours ago

Lorenzo LiveraniLorenzo Liverani

243

asked 15 hours ago

Lorenzo LiveraniLorenzo Liverani

243