This theorem, due to M. Baire, is beyond the scope of our subject. However, on one hand, we will use the necessary condition it expresses, and on the other hand, and most importantly, the transfinite method that we will use to prove that the stated condition is sufficient, is the very same method which allowed M. Denjoy to completely solve the problem of primitive functions. Also, we will henceforth consistently use transfinite numbers. Readers who are not familiar with the use of these numbers should study the Note located at the end of the volume before reading this chapter.

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The Totalisation

  • Rahul Jain

摘要

This theorem, due to M. Baire, is beyond the scope of our subject. However, on one hand, we will use the necessary condition it expresses, and on the other hand, and most importantly, the transfinite method that we will use to prove that the stated condition is sufficient, is the very same method which allowed M. Denjoy to completely solve the problem of primitive functions. Also, we will henceforth consistently use transfinite numbers. Readers who are not familiar with the use of these numbers should study the Note located at the end of the volume before reading this chapter.