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Un criterio di completa additività per le funzioni aritmetiche riguardante successioni di densità irregolare

Fulvia Skof — 1970

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Let f ( n ) be an additive number-theoretical function. A sufficient condition is given for complete additivity of f ( n ) : this condition, involving the behaviour of δ ( n ) = f ( n + 1 ) - f ( n ) , requires δ ( u ) 0 as u + throughout an increasing sequence of positive integers u , having “upper density” I (i.e. ( lim sup ( I : u x ) / x = I ) and not necessarily “density” I.

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