Acts 10:42

“ And he charged us to preach to the people, and to testify that this is he who is ordained of God to be the Judge of the living and the dead.”

Having risen He had then given a charge to His Apostles to preach to the people, testifying that God had ordained Jesus as Judge of the living and the dead, and was thus establishing His Heavenly Kingship and His Kingly Rule.

So, although containing here a little more detail about His life because of the type of audience, the usual pattern of Peter's speeches is repeated; life of Jesus, death of Jesus, resurrection of Jesus, exaltation of Jesus; prophetic backing.

‘Preach to the people.' Some would see this as referring to the people of Israel, but Acts 10:43 expands this to mean ‘all who believe'. There is no real reason why this cannot signify the Apostolic responsibility to proclaim the Good News to all people in the whole creation (Luke 22:47; Mark 16:15; Matthew 28:19), especially in view of Peter's recent vision.

“The Judge of the living and the dead.” We can compare here Acts 17:31; Genesis 18:25; Deuteronomy 32:4; Isaiah 11:4; Isaiah 42:4; John 5:22; John 5:27. Here His rule and authority has clearly been established over earth and heaven (compare Matthew 28:18), for those who judged were those who ruled.