They are only very loosely connected, if at all. Their only common point is Asimov's idea of a future galactic empire, and this is barely mentioned in Pebble in the Sky.
Asimov later integrated them into his all-engulfing Foundation series. Some contortion was required to explain how the robots of the Elijah Bailey[?] novels are almost completely absent from the Empire novels. In reality, this was due to the magazine editor Asimov worked with at the time (John W. Campbell) disliking robots in science fiction, and discouraging (forbidding?) Asimov from including them.
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