A Selective Survey of Ideas, Tools and Results in Constructive QFT II

In this talk we continue to discuss the constructive programme in rigorous QFT. Our aim is discuss a few points on difficulties in relation to the definition of Euclidean path integrals and the general strategy of constructive field theory from a constructive perspective. This will motivate a discussion of the fundamental results in probability theory which are the main tools for the construction of Euclidean path integral measures. We might also discuss some points in relation to free fields, including in particular difficulties in the characterisation of massless fields.