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converges, Frostman [1] has shown that it also converges absolutely almost everywhere on {z: I z = 1). It will be shown here that if (1) does not converge then the arguments of the terms of the sequence fan} can be so chosen that B(z,{an}) diverges whenever lzl = 1. Although I am not aware of the existence, in the published literature, of examples of Blaschke products which diverge everywhere on {z: lzl = 11, some unpublished examples have been obtained by Clunie and Piranian.

On Blaschke products diverging everywhere on the boundary of the unit disc