Re: lebesgue

On 21 Şubat, 14:27, The World Wide Wade <aderamey.a...@xxxxxxxxxxx>
wrote:
In article
<432dbdab-0a93-4a80-9764-b47235105...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,





 v_aylin2...@xxxxxxxxxxx wrote:
On 21 Șubat, 13:06, Robert Israel
<isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
v_aylin2...@xxxxxxxxxxx writes:
f is a nonnegative and integrable over a measurable set E. Then
epsilon greater than 0 and delta greater than 0 s.t. over a measurable
set A subset of E with
lamda(A)<delta, we have integral_A f d lambda < epsilon

it means A has measure zero.If A has measure zero we can say lambdaA=0
then,
lambdaA=0 and f is measurable integral_R f X_A dlambda=0

we know that if A subset of E
integral_A f dlambda= integral_R X_A f dlambda<=integral_R X_E
dlambda=
integral_E f dlambda

from this
0<= integral_R X_E dlambda=integral_E f dlambda

What should I do now?

That depends on what you're trying to do, which is not at all clear.
What exactly is the problem you're trying to solve?  Please be careful
to include the quantifiers (for all) and (there exists), and in the correct
order: they are very important.
--
Robert Israel              isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada- Alıntıyı
gizle -

- Alıntıyı göster -

I'm trying to show that

∫f dlambda<epsilon
A

State the problem precisely.- Alıntıyı gizle -

- Alıntıyı göster -

f is a nonnegative and integrable over a measurable set E. Then є>0
and δ>0 s.t. over a measurable
set A subset of E with λ(A)<δ, show that ∫fdλ<є
A




.

Relevant Pages

  • Re: lebesgue
    ... epsilon greater than 0 and delta greater than 0 s.t. over a measurable ... integral_E f dlambda ... but I suspect it shows a basic lack ...
    (sci.math)
  • Re: lebesgue
    ... epsilon greater than 0 and delta greater than 0 s.t. over a measurable ... integral_E f dlambda ... but I suspect it shows a basic lack ...
    (sci.math)
  • Re: lebesgue
    ... epsilon greater than 0 and delta greater than 0 s.t. over a measurable ... integral_E f dlambda ... of understanding of the mathematics. ...
    (sci.math)
  • Re: lebesgue
    ... epsilon greater than 0 and delta greater than 0 s.t. over a measurable ... integral_E f dlambda ...
    (sci.math)
  • Re: lebesgue
    ... epsilon greater than 0 and delta greater than 0 s.t. over a measurable ... integral_E f dlambda ...
    (sci.math)
Quantcast