A submeasure θ on a Boolean algebra B is pathological if it does not dominate a positive finitely additive functional. It is ε-exhaustive if every sequence {An} of pairwise disjoint sets in B satisfies lim supn θ(An) ≤ ε. It is exhaustive if it is 0-exhaustive. It is normalized if θ(1B) = 1. Question 1. Is there a normalized exhaustive pathological submeasure on the algebra of clopen subsets of the Cantor space?