Question From Disadvantage of SVM classifier (disadvantages of convex hull of SVM classifier)

I'am reading about the disadvantages of SVM classifier.in this article : 'hyperdisk based large margin classifier(2013 Hakan Cevikalp, Bill Triggs)' authors mention some reasons about the failure of convex hull of SVMs in approximate the true extent of class's. I write their reason's with no changing from their article:

• "Unfortunately, in high-dimensional spaces, the convex hull of any sub-exponential number of training samples from a convex set typically has a volume that is exponentially smaller than that of the parent set. For example, this is the case for the simplex spanning any set of d+1 points sampled from an ellipsoid or box in d dimensions: the overwhelming majority of the set lies outside the given simplex, and a new sample from it will almost surely lie well outside the simplex in some direction. Similarly, for Gaussian's, the convex hull of any probable placement of a sub-exponential number of samples contains exponentially little of the probability mass."

I have 4 questions:

1- what is the meaning of sub-exponential number of a set X?(if it is possible please explain it with simple example)

2- what is the simplex spanning of a set X?

3- what is the meaning of this sentence:"this is the case for the simplex spanning any set of d+1 points sampled from an ellipsoid or box in d dimensions" ???

4- what is the meaning of this sentence:"Similarly, for Gaussian's, the convex hull of any probable placement of a sub-exponential number of samples contains exponentially little of the probability mass"???

 thank you for your attention.