I'm baack... (too late to phone in sick). It seems the [experiment](http://mathoverflow.net/questions/61270/infinitesimal-generators-of-stochastic-processes) as originally intended has been performed to sufficient precision by one Wolfgang Arendt in 1984...

So... I was sick, and had this 3rd idea of proof and ventured into combining Vitali's theorem on stochastic convergence with Banach-Alaoglu. And yet I didn't make it to the internets box (let alone boot my crazy offline laptop) to update said wiki page. At least, in the parallel universe of my micro paper works it is verified that I haven't saved Shigekawa's 1st preprint (incl. his proof, perhaps giving the idea, other than Barry Simon's simpler proof via resolventics.)...

**Of all this** a lemma remains (the only thing my mathematical experimentations produced) which questions the common definition of the signum _functional_ (not always linear). So, the experiment might go on...

Will write up later, so the plan.

So... I was sick, and had this 3rd idea of proof and ventured into combining Vitali's theorem on stochastic convergence with Banach-Alaoglu. And yet I didn't make it to the internets box (let alone boot my crazy offline laptop) to update said wiki page. At least, in the parallel universe of my micro paper works it is verified that I haven't saved Shigekawa's 1st preprint (incl. his proof, perhaps giving the idea, other than Barry Simon's simpler proof via resolventics.)...

**Of all this** a lemma remains (the only thing my mathematical experimentations produced) which questions the common definition of the signum _functional_ (not always linear). So, the experiment might go on...

Will write up later, so the plan.