Abstract Some features of the notion sufficiency in quantum statistics are investigated. Three kinds this considered: plain (called simply: sufficiency), strong and Umegaki’s sufficiency. It is shown that for a finite von Neumann algebra with faithful family normal states minimal sufficient subalgebra sense. Moreover, proper version factorization theorem Jenčová Petz obtained. The structure des...

Increasing input self-sufficiency is often viewed as a target to improve sustainability of dairy farms. However, few studies have specifically analysed input self-sufficiency, by including several technical inputs and without only focussing on animal feeding, in order to explore its impact on farm sustainability. To address this gap, our work has three objectives as follows: (1) identifying the...