In this final talk of the series, I have two overall goals. First, I will look at some alternatives to Martin-Lof's notion of randomness, and explain the relationships among the different concepts, using martingales as a common thread. Second, I will discuss (in not too fine detail) certain effective versions of classical probabilistic laws, for various of the randomness notions presented. This extends the discussion begun in the previous talk, in which Jason Rute presented the result that the strong law of large numbers holds for every Martin-Lof random sequence.

This is the the third in a series of talks by Ed Dean and Jason Rute.