On the least primitive root of a prime

Abstract

October 0 <t -x < 1/n implies [F(t) -F(x)]/(t -x) ^ n; the remainder of the proof.isunaltered.The next lemma is a slight generalization of a theorem of Marcinkiewicz.LEMMA 5.2.If f(x) is measurable on [a, b], and has either a left major or a right major, and also has either a left minor or a right minor, then f (x) is Perron integrable on [a, b].The proof is that given by Saks, op.cit., p. 253; the principal change is that the reference to his Theorem 10.1 is replaced by a reference to our Lemma 5.1.Since every P*-integrable function ƒ(#) is measurable and has right majors and right minors, it is also Perron integrable by Lemma 5.2, and the equivalence of the integrals is established.

Locations

• Project Euclid (Cornell University) - View - PDF
• Bulletin of the American Mathematical Society - View - PDF