Talk:Piecewise Continuous Function with One-Sided Limits is Darboux Integrable

Is "Additivity with respect to Interval of Integration" perhaps a reference to Sum of Integrals on Adjacent Intervals? &mdash; Lord_Farin (talk) 08:52, 27 September 2013 (UTC)


 * No. "Additivity with respect to Interval of Integration" presupposes that two of the three integrals exist whereas "Sum of Integrals on Adjacent Intervals" presupposes that the common integrand is continuous. Ivar Sand (talk) 09:17, 27 September 2013 (UTC)


 * The hypotheses may not match, but the proof certainly follows through for any $f$ satisfying your hypotheses. &mdash; Lord_Farin (talk) 09:21, 27 September 2013 (UTC)


 * It seems to me that in the proof of "Sum of Integrals on Adjacent Intervals" one needs the existence of the integral from a to b, and this is assured by the continuity of $f$. In our case, we need to prove that the integral from a to b exists. Ivar Sand (talk) 09:52, 27 September 2013 (UTC)


 * There is indeed some work to be done. I'll put up a call to Template:Expand. &mdash; Lord_Farin (talk) 09:58, 27 September 2013 (UTC)

I intended "Integrable" and not "integrable" in the title so this is an error. Sorry! Please correct the error. Ivar Sand (talk) 09:54, 27 September 2013 (UTC)


 * Done. &mdash; Lord_Farin (talk) 09:58, 27 September 2013 (UTC)

Does the suggestion "The result referenced from Apostol is to be extracted and put into 𝖯𝗋∞𝖿𝖶𝗂𝗄𝗂 in its own right" mean that Apostol's book is not copyright protected any more?--Ivar Sand (talk) 08:59, 10 March 2015 (UTC)


 * It means that all results referenced on must themselves be results on {{ProofWiki}. It is doubtful that a proof at this level is genuinely the intellectual property of Apostol (I am sure that these results have been kicking around since a lot longer than from 1967), so the construction of the proof cannot be considered as subject to copyright laws. --prime mover (talk) 10:45, 10 March 2015 (UTC)