This note introduces the basic concepts and definitions of measure theory relevant to probability theory. It is meant to be a simplified tutorial on measure theory.

Exploring the phenomenon of surface cracks and abnormal ground behavior during coal mining under gully landforms, laboratory physical similarity simulation models were established to study movement characteristics laws working faces different methods landforms. The results indicate that in cases when a roadway is situated below top slope, corresponding deformation surrounding rock aggravated by...

Afforestation is an approach for ecological restoration. Soil total phosphorus one of the important and evolutionary elements carbon cycles plant growth following afforestation. However, studies on soil afforestation abandoned ponds with different slopes are still lacking. other properties from sites were investigated. phosphorus, nitrogen, bulk density, water contents pH poplar ( Populus spp.)...

If S is an arbitrary sequence of positive integers, let P(S) be the set of all integers which are representable as a sum of distinct terms of S . Call S complete if P(S) contains all large integers, and subcomplete if P(S) contains an infinite arithmetic progression . It is shown that any sequence can be perturbed in a rather moderate way into a sequence which is not subcomplete . On the other ...

This article provides a brief survey of the literature on unawareness and introduces the contributions to the special issue on unawareness in Mathematical Social Sciences. First, we provide a brief overview both about epistemic models of unawareness and models of extensive-form games with unawareness. Instead of introducing the approaches in full detail, we illustrate the main differences and s...