We prove theorems which imply the following results. (1) " M o s t " almost periodic functions b (t) with unbounded integral oscillate in a strong sense. (2) If B is a continuous function on a minimal flow (I"~,R), then either the time averages (1/t)f'oB(oJ. s)ds all converge, or they diverge on a residual set.
Minimal functions with unbounded integral / R. Johnson. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - STAMPA. - 31:(1978), pp. 133-141. [10.1007/BF02760544]
Minimal functions with unbounded integral
JOHNSON, RUSSELL ALLAN
1978
Abstract
We prove theorems which imply the following results. (1) " M o s t " almost periodic functions b (t) with unbounded integral oscillate in a strong sense. (2) If B is a continuous function on a minimal flow (I"~,R), then either the time averages (1/t)f'oB(oJ. s)ds all converge, or they diverge on a residual set.
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