Timeline for The Fundamental Theorem of Calculus in Lebesgue Theory
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 10, 2018 at 14:05 | comment | added | LSpice | A useless note from the future: the "fundamental theorem of calculus" and the "backwards fundamental theorem of calculus" are both called the FTC, usually FTC1 and FTC2, at least in calculus textbooks. (I'm not sure that's true in Lebesgue-integration textbooks.) How anyone can remember which is 1 and which is 2 I don't know. | |
| Jul 20, 2010 at 3:06 | vote | accept | Max Menzies | ||
| Jul 14, 2010 at 15:31 | comment | added | Daniel Litt | @Pete L. Clark: Ah, I see. I was thinking of the usual counterexamples to $I\circ D$ in the case of Riemann integration, but I suppose asking when the "backwards fundamental theorem of calculus" (the CTF?) holds is an interesting question. | |
| Jul 14, 2010 at 15:16 | comment | added | Pete L. Clark | @Daniel: Since differentiation and integration are supposed to be essentially mutually inverse operators, there are two parts to the fundamental theorem of calculus, one for $D \circ I$ and the other for $I \circ D$. These two cases turn out to be related but distinct (see e.g. my commentson the Mean Value Theorem question). The OP is asking about $I \circ D$. | |
| Jul 14, 2010 at 13:20 | history | answered | Daniel Litt | CC BY-SA 2.5 |