Re: How to Prove m_j*=m*. (Latex code)
- From: David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx>
- Date: Fri, 18 Jan 2008 07:16:22 -0600
On Thu, 17 Jan 2008 04:10:56 -0800 (PST), water
<waterloo2005@xxxxxxxxx> wrote:
On 1?17?, ??8?02?, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On Wed, 16 Jan 2008 08:30:43 -0800 (PST), water
<waterloo2...@xxxxxxxxx> wrote:
On 1?16?, ??10?37?, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On Tue, 15 Jan 2008 21:26:45 -0800 (PST), water
<waterloo2...@xxxxxxxxx> wrote:
On 1ÔÂ16ÈÕ, ÉÏÎç8ʱ15·Ö, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On Tue, 15 Jan 2008 01:55:24 -0800 (PST), water
<waterloo2...@xxxxxxxxx> wrote:
$\mathcal{R}_J$ is class of Jordan measurable set. $R$ is real line.
$\forall E\in R, m_J^*(E) = \inf \{\sum_{i = 1}^{\infty} m_J(E_i) | E_i
\in \mathcal{R}_J, E\subset \cup_{i = 1}^\infty E_i\}$.
$\mathcal{R}_0 = \{\cup_{i = 1}^n (a_i,b_i] | a_i\leq b_i ,i =
1,\cdots,n\}$
Lebesgue measure of set in $\mathcal{R}_0$ is : $m((a,b]) = b - a$.
$m^*$ is induced outer measure of Lebesgue measure in $\mathcal{R}_0$.
$\forall E\in R,m^*(E) = \inf \{\sum_{i = 1}^{\infty} m(E_i) | E_i\in
\mathcal{R}_0, E\subset \cup_{i = 1}^\infty E_i\}$.
$\forall E\in \mathcal{R_J}, m_J(E) = m_J(E^\circ \cup \partial E) =
m(E^\circ) = m(E^\circ\cup\partial E) = m(E)$.
How to prove $\forall E\in R, m_J^*(E) = m^*(E)$.
Excuse me! I don't know how to input complex math formular in plain
text.
Some would say that when you're new to a newsgroup you should
read a few posts first to get an idea of the local conventions.
It's really not that hard to post those formulas in a way that;s
much easier for humans to read - we do it all the time.
Can you help me prove the lemma? Thanks
************************
David C. Ullrich- Òþ²Ø±»ÒýÓÃÎÄ×Ö -
- ÏÔʾÒýÓõÄÎÄ×Ö -
A friendly output can be found at:
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=183377
Fabulous. You probably got an answer there too, right?
************************
David C. Ullrich- ??????? -
- ??????? -
I am stupid. Can you say more?
Ok - I thought what I was trying to say was clear, but
I'll be more explicit. It's a good thing to respect
the local customs in a place like a newsgroup,
especially when there's a reason for them (all those
dollar signs and \mathcal's above only make your
post harder to read). And it's also not a good thing
to post a link to a question, expecting the reader
to go somewhere else just for the sheer joy of
being able to help you with your question - if you
have a question to ask sci.math you should post the
question to sci.math.
************************
David C. Ullrich- ??????? -
- ??????? -
but express math formular in ASCII is difficult.
where can I find instructions of that?
For the third time: If you're new to sci.math you
should start by reading some posts in sci.math!
You won't find "instructions", but you'll see
people expressing complicated formulas all the time.
Or: Take the TeX you want to post, and remove everything
that has no _mathematical_ content. That means the dollar
signs, the things that specify fonts, etc. int_0^1
instead of $\int_0^1$. int_R instead of $\int_{\mathcall R}$.
Etc.
************************
David C. Ullrich
.
- References:
- How to Prove m_j*=m*. (Latex code)
- From: water
- Re: How to Prove m_j*=m*. (Latex code)
- From: David C . Ullrich
- Re: How to Prove m_j*=m*. (Latex code)
- From: water
- Re: How to Prove m_j*=m*. (Latex code)
- From: David C . Ullrich
- Re: How to Prove m_j*=m*. (Latex code)
- From: water
- Re: How to Prove m_j*=m*. (Latex code)
- From: David C . Ullrich
- Re: How to Prove m_j*=m*. (Latex code)
- From: water
- How to Prove m_j*=m*. (Latex code)
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