Re: How to prove that the space of signed measures is complete?
On 11 Aug, 09:20, victor_meldrew_...@xxxxxxxxxxx wrote:
As the sequene (m_n) is Cauchy, it has a subsequence
(m'_n) with ||m'_n-m'_{n+1}|| < 1/2^n.
We may as well replace (m_n) by (m_{n+1}).
Now set s_n = m_{n+1} - m_n. Now we are effectively
looking at the sum m_1 + s_1 + s_2 + ... of measures.
Now the question is can we reverse order of summation in
the double sum of s_k(A_i)?
But sum_i |s_k(A_i)| <= ||s_k|| <+ 1/2^k so
that sum_k sum_i |s_k(A_i)| is finite.
This allows us to swap the order of summation.
That looks sound. Thanks.
.
Relevant Pages
- Re: Infinite Factorial & Regularization
... >concept called Borel summation. ... and you try to sum the Taylor series obtained by taking derivatives ... like every quantum field theory class, ... region, you need Abel summation. ...
(sci.math) - Re: OT - My summation of Tedious
... A sum or aggregate. ... Here is the difference BTB, i knew the meaning from my education, you only know the meaning after running to Google, and now, in a vain attempt to look good, are trying to use that 'Google knowledge' to get one over on me LOL ... Your education says summation is limited to number sums. ... No summation was one word you could of used as well as summary. ...
(uk.sport.football.clubs.liverpool) - Re: OT - My summation of Tedious
... A sum or aggregate. ... Your education says summation is limited to number sums. ... No summation was one word you could of used as well as summary. ... Now fuck off. ...
(uk.sport.football.clubs.liverpool) - Re: OT - My summation of Tedious
... A sum or aggregate. ... Here is the difference BTB, i knew the meaning from my education, you only know the meaning after running to Google, and now, in a vain attempt to look good, are trying to use that 'Google knowledge' to get one over on me LOL ... Your education says summation is limited to number sums. ... No summation was one word you could of used as well as summary. ...
(uk.sport.football.clubs.liverpool) - Re: OT - My summation of Tedious
... A sum or aggregate. ... Here is the difference BTB, i knew the meaning from my education, you only know the meaning after running to Google, and now, in a vain attempt to look good, are trying to use that 'Google knowledge' to get one over on me LOL ... Your education says summation is limited to number sums. ... No summation was one word you could of used as well as summary. ...
(uk.sport.football.clubs.liverpool) |
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