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.
oedipus says that his fame is widespread and the world knows the deeds which he had performed.