… an additive function h (ie a function such that h(:v+y) = h(w)+h(y) for all m, y) such that f(m) =
h(a;) for almost all 9; (“almost all… In this note we shall show that the answer is affirmative (see …

… = Fs(x) Js-almost everywhere in 5. Further, according to [1, Theorem 3], Fs can be extended
to an additive function F: G —» H in a unique way. Since Js C J, we have f(x) = i^a:) J-almost …

… that has no carrier, even though it vanishes on almost all sets. … 20 To prove the first part
of the second statement, we note that ,/^|fI must vanish for all subsets of N, since the absolute …

… an individual term of the almost-periodic development under … theory of monotone absolutely
additive set functions,** which … Finally, we note that although G, was defined as an iterated …

… Such functions are called sub-additive. If the inequality is reversed, the functions will be
termed super-additive. Subadditive functions in E have been treated fully by Hille [10; Chapter VII…

… holds for almost all pairs (x, y)~ R 2 (an almost additive function). Does there exist an
additive function g:R ~ R such that f(x)= g(x) for almost all x ~ R? NG de Bruijn [1] (and, …

… We note that <b+ and 0_ must both vanish for all bounded sets if <j> does so. Using An as (…
for almost all a-\-v and equals x(a-\-v). Thus, a being fixed, the limit 3.6.4 exists for almost all v …

… a>(p—1) is log logp; that is to say, that for almost all p, o)(p—l) is approximately equal to
loglogp. … The object of this note is to prove in Part I the following improvement of Prachar's result: …

Let f (m) be a real valued number theoretic function. We say that it is addi-tive if for (mn, iM2)=
1, f (m1 i M2)= f (ml)+ f (m2). Denote by N (f; c, n) the number of integers m< n for which f (m…

… We also note that … almost additive and asymptotically additive conditions remain very
relevant for applications: by Theorem 1.2, they can be seen as sufficient conditions for the additive …