0

Forgive me for the vague question. Several years ago, I read about a theorem that (if I remember well) proved what is written in the title. I guess the theorem is from Wiener and it seemed that this theorem was present in his book "The Fourier integral and certain of its applications". But I can't find it anywhere. I could be mistaken in my attribution though.

I've been Googling for several days and I couldn't find it. Perhaps I don't remember it too well, perhaps me having to translate from my native language has caused some trouble, etc.

Red Banana
  • 24,885
  • 21
  • 101
  • 207
  • There are famous examples related to physics and Maxwell's equations (Green's theorem, divergence theorem, curl theorem), like the 1-d line integral of current around a closed curve is related to the 2-d integral of magnetic field through the curve. You can check wikipedia, or a coffee mug, for Maxwell's equations. The Cauchy integral formula is also in this genre. – Michael May 08 '19 at 19:11
  • @Michael Yes, I know them. But it was something bigger, I guess. It was about any number of integrals could be transformed into a single integral. – Red Banana May 08 '19 at 19:13
  • If $\int_0^1 g_i(x)dx = m_i$ for $i \in {1, …, n}$ then $$\int_0^n\left[\sum_{i=1}^n g_i(x-i+1)1_{{x \in [i-1, i) }}\right]dx=\sum_{i=1}^n m_i$$ =) – Michael May 08 '19 at 19:16
  • @Michael I guess I found it! Look at this. – Red Banana May 08 '19 at 19:43
  • Aha. I see that link has an unanswered question. If space-filling curves can be (in principle) used, I doubt they would make anything easier. – Michael May 08 '19 at 23:03
  • @Michael Yes. It seems there are more details about it on Hans Sagan's "Space-Filling Curves". – Red Banana May 08 '19 at 23:04

0 Answers0