Referring to the things fulfilled, implies they were predicted in the Old Testament.  Time and time again Luke refers back to what prophets in the Old Testament had predicted about the Messiah who was to come.  Jesus Himself quoted a prophecy early in His public ministry while in the synagogue in Nazareth, “The Spirit of the Lord is on me, because he has anointed me to preach good news to the poor.  He has sent me to proclaim freedom for the prisoners and recovery of sight for the blind, to release the oppressed, to proclaim the year of the Lord’s favor.”  The eyes of everyone present that day were riveted on Him.  Then He said, “Today this scripture is fulfilled in your hearing.” 

The Gospel of Luke describes how Jesus lived out this affirmation of His Messiahship and how people responded to or rejected it.  That is why Luke was careful to investigate everything from the beginning that was available to him from eyewitnesses and written accounts of these events.  Luke wanted Theophilus to know the certainty of the things he had been taught.  And what Luke wrote, God has used over the centuries to enrich countless lives.