What does Oedipus mean when says "The world knows my fame; I am Oedipus."

I think that Oedipus' statement reflects the level of
tragic proportions within his narrative.  In terms of what he means by the statement in
the opening, it is a boastful declaration of free will.  Oedipus asserts his own
authority, and his own sense of self in the statement.  In this statement is the
fundamental assertion of his power, his rule as king, and the endeavors in which he has
done that represent his greatness.  At the start of the drama, his "fame" represents to
which ends his free will has been accomplished.  This is a stark contrast to the end of
the drama, in which the forces of fate have overcome Oedipus.  The ending of the drama
represents the sum totality of Oedipus' failures, a condition that is the opposite of
his beliefs at the start of the drama.  At the drama's conclusion, Oedipus will be known
by the world.  However, this fame is more infamy and representation of how he will
become the cautionary tale for hubris and the belief that free will can overcome the
powers of fate and the divine.  In this acknowledgement, there is a severe level of
acceptance of one's failures and the drop from being glorious to being
pathetic.