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285 |
285 |
286 ``The usual assumption in complex analysis texts is that a path \<open>\<gamma>\<close> should be piecewise |
286 ``The usual assumption in complex analysis texts is that a path \<open>\<gamma>\<close> should be piecewise |
287 continuously differentiable, which ensures that the path integral exists at least for any continuous |
287 continuously differentiable, which ensures that the path integral exists at least for any continuous |
288 f, since all piecewise continuous functions are integrable. However, our notion of validity is |
288 f, since all piecewise continuous functions are integrable. However, our notion of validity is |
289 weaker, just piecewise differentiability... [namely] continuity plus differentiability except on a |
289 weaker, just piecewise differentiability... [namely] continuity plus differentiability except on a |
290 finite set ... [Our] underlying theory of integration is the Kurzweil-Henstock theory. In contrast to |
290 finite set ... [Our] underlying theory of integration is the Kurzweil-Henstock theory. In contrast to |
291 the Riemann or Lebesgue theory (but in common with a simple notion based on antiderivatives), this |
291 the Riemann or Lebesgue theory (but in common with a simple notion based on antiderivatives), this |
292 can integrate all derivatives.'' |
292 can integrate all derivatives.'' |
293 |
293 |
294 "Formalizing basic complex analysis." From Insight to Proof: Festschrift in Honour of Andrzej Trybulec. |
294 "Formalizing basic complex analysis." From Insight to Proof: Festschrift in Honour of Andrzej Trybulec. |
295 Studies in Logic, Grammar and Rhetoric 10.23 (2007): 151-165. |
295 Studies in Logic, Grammar and Rhetoric 10.23 (2007): 151-165. |