The Lindley paradox, information and generalized functions

In testing a sharp point hypothesis there is a difference between frequentist and Bayesian results. Even for sample sizes increasing to infinity, Bayesian methods accept the point null hypothesis for values where the frequentist method leads to rejection. This is called the Lindley paradox. Here it is attempted to explain this. The reason appears to be not a specific feature of Bayesian methods, but a misuse of the theorem of Bayes.