Generic non-singular Poisson suspension is of type III1

It is shown that for a dense $G_\delta $ -subset of the subgroup of non-singular transformations (of a standard infinite $\sigma $ -finite measure space) whose Poisson suspensions are non-singular, the corresponding Poisson suspensions are ergodic and of Krieger’s type III1.

Importance of Fenestration Size for Definitive Treatment of a Quadrigeminal Arachnoid Cyst: Endoscopic Inspection of the Cyst and Surrounding Anatomy: 2-Dimensional Operative Video

Arachnoid cysts are fluid-filled sacs, located between the brain or spinal cord and the arachnoid membrane. Their prevalence in children is between 1% and 3%. Quadrigeminal arachnoid cysts represent 1% to 10% of them and are often associated with hydrocephalus, mostly by an obstructive mechanism, explained by compression of the tectum of the midbrain. When an indication for treatment is retained, 3 surgical options are available: microsurgical excision/fenestration, endoscopic fenestration, and shunt placement. Endoscopic treatment is considered the best compromise of definitive treatment with least surgical morbidity, especially because quadrigeminal cysts are located close to the midline, in intimate relationships with basal cisterns and ventricles. We here present the endoscopic treatment of a prenatally diagnosed quadrigeminal arachnoid cyst type III1 with right lateral extension into the middle cerebral fossa, and associated hydrocephalus, treated at the age of 18 mo. Step-by-step detail of surgical technique is presented in original anatomic conditions. Restoration of better cerebrospinal fluid pathways being the objective of this surgery, ventriculocystic, and cyst-cisternal fenestrations were made. Secondary obstruction of the cyst occurred a few months later, requiring further endoscopic treatment to obtain a larger fenestration that allowed good long-term clinical and radiological outcome. The key point of this video is to compare the 2 procedures, stressing the importance of the dimension of fenestrations, to ensure a long-term patency of both stomas. The patient being a child, both parents gave their consent for publication and signed a form.

Classification of Roberts actions of strongly amenable C∗-tensor categories on the injective factor of type III1

In this paper, we generalize Izumi’s result on uniqueness of realization of finite C[Formula: see text]-tensor categories in the endomorphism category of the injective factor of type III1 for finitely generated strongly amenable C[Formula: see text]-tensor categories by applying Popa’s classification theorem of strongly amenable subfactors of type III1.

On a type III1 Bernoulli shift

We construct a product measure under which the shift on {0,1}ℤ is a type III1 transformation.