What is the Greeks' view about destiny in light of Oedipus Rex by Sophocles?

The only reason the oracle at Delphi can offer Oedipus a prophecy regarding his future—that he will kill his father and marry his mother—is because his fate is already determined.  Throughout the play, it does not matter what Oedipus does; it seems as though he is on a fast train toward the destiny he tries so hard to avoid.  Even before the play begins, he had made the decision not to return to Corinth, where...

The only reason the oracle at Delphi can offer Oedipus a prophecy regarding his future—that he will kill his father and marry his mother—is because his fate is already determined.  Throughout the play, it does not matter what Oedipus does; it seems as though he is on a fast train toward the destiny he tries so hard to avoid.  Even before the play begins, he had made the decision not to return to Corinth, where he believes his mother and father live (so that he cannot possibly kill him and wed her).  Instead, he decides to make his way to Thebes, not realizing that his biological parents, Laius and Jocasta, live there.  In other words, Oedipus's attempts to avoid his fate actually allows it to come to be; this makes it seem as though his choices have no real impact because—no matter what actions he takes—they lead to the destiny that has already been laid out for him.