Signified (esēmainen). Imperfect active in Westcott and Hort, but aorist active esēmānen in the margin. The verb is an old one from sēma (sēmeion) a sign (cf. the symbolic sign in Act 21:11). Here Agabus (also in Act 21:10) does predict a famine through the Holy Spirit.
Should be (mellein esesthai). Mellō occurs either with the present infinitive (Act 16:27), the aorist infinitive (Act 12:6), or the future as here and Act 24:15; Act 27:10.
Over all the world (eph' holēn tēn oikoumenēn). Over all the inhabited earth (gēn, understood). Probably a common hyperbole for the Roman empire as in Luk 2:1. Josephus (Ant. VIII. 13, 4) appears to restrict it to Palestine.
In the days of Claudius (epi Klaudiou). He was Roman Emperor a.d. 41-44. The Roman writers (Suetonius, Dio Cassius, Tacitus) all tell of dearths (assiduae sterilitates) during the brief reign of Claudius who was preceded by Caligula and followed by Nero.