Lectures on Gleason Parts

Standing assumptions and notations.- Examples of Gleason parts.- Proof of the d-?-G identity.- Geometric description of parts in TB.- Representing measures and parts in TC.- Inner parts and their associated normed spaces.- Selection of mutually absolutely continuous representing measures.- Integral kernels.- Geometric properties of d and a continuous selection theorem.- Completeness of the part metric.- Linear functionals as differences of positive functionals.