In this paper, we derive a new form of weak laws of large numbers for sub-linear expectation and establish the equivalence relation among this new form and the other two forms of weak laws of large numbers for sub-linear expectation. Moreover, we obtain the strong laws of large numbers for sub-linear expectation under a general moment condition by applying our new weak laws of large numbers.

In this paper, we investigate some strong laws of large numbers for sub-linear expectation without independence which generalize the classical ones. We give some strong laws of large numbers for sub-linear expectation on some moment conditions with respect to the partial sum and some conditions similar to Petrov’s. We can reduce the conclusion to a simple form when the the sequence of random variables is i.i.d. We also show a strong law of large numbers for sub-linear expectation with assumptions of quasi-surely.

In this paper, we derive the weak and strong results of Marcinkiewicz–Zygmund laws of large numbers under sublinear expectation. The results are extensions of the Kolmogorov laws of large numbers under sublinear expectation and the classical Marcinkiewicz–Zygmund laws of large numbers.

Stabilization technology is widely used in the remediation of heavy metal-contaminated farmland soil. However, the evaluation method for the remediation effect is not satisfactory. To scientifically evaluate the remediation effect, this study constructed a comprehensive evaluation system by bibliometric analysis and an analytic hierarchy process (AHP). Ultimately, 16 indicators were selected from three aspects of the soil, crops, and amendment. The 16 indicators are divided into three groups, namely indicators I that can be evaluated according to the national standards of China, indicators II that can be evaluated according to the classification management of farmland and Indicators III that are the dynamic change indicators without an evaluation criterion. Comprehensive scores for 16 indicators were calculated using three response models, respectively. According to the difference between the scores before and after the remediation, the remediation effect is divided into five levels, which are excellent, good, qualified, poor, and very poor. This study provides a theoretical basis and insightful information for a farmland pollution remediation and a sustainable utilization.