Before revision: A fundamental problem in linear programming, machine learning, and computational geometry is the  Convex Hull Membership (CHM)  : Given a point p and a subset S of n points in R^m, is p \in conv(S)?
After revision: A fundamental problem in linear programming, machine learning, and computational geometry is the Convex Hull Membership (CHM) problem is : Given a point p and a subset S of n points in R^m, is p \in conv(S)?