'Investigation' in the Bible

it has seemed right to me also, after careful investigation of the facts from their commencement, to write for you, most noble Theophilus, a connected account,

Now therefore, you and the Council notify the commander to bring him down to you, as though you were going to determine his case by a more thorough investigation; and we for our part are ready to slay him before he comes near the place.”

And [because] I was at a loss with regard to the investigation concerning these [things], I asked if he was willing to go to Jerusalem and to be judged there concerning these [things].

Yet I have nothing definite about him to write to my lord. Therefore I have brought him before you all and especially before you, King Agrippa, so that after the investigation has taken place, I may have something to write.