Extreme value theory focus on studying extremal behaviors of random phenomenons. In the first part of the talk, I will introduce stable distributions and stable subordinators. They appear naturally when people consider questions in a heavy-tailed setting. For the second part of the talk, I will introduce Poisson point processes and random sup measures. These two notions have intrinsic connections with extremal value theory, which I will explain. In the last part, I am going to construct a random sup-measure with long range dependence. This random sup-measure incorporates a special point processes and the stable subordinators. And we will see how it diers from the memoryless cases. Background in probability theory is useful but not necessary. Everyone is welcome to this talk.