In this paper, we prove that every F ∗ space (i.e., Hausdorff topological vector space satisfying the first countable axiom) can be characterized by means of its “standard generating family of pseudo-norms”. By using the standard generating family of pseudo-norms P, the concepts of P-bounded set and γ-maxpseudo-norm-subadditive operator in F ∗ space are introduced. The uniform boundedness princ...

Abstract. We investigate uniform ergodic type theorems for additive and subadditive functions on a subshift over a finite alphabet. We show that every strictly ergodic subshift admits a uniform ergodic theorem for Banach-spacevalued additive functions. We then give a necessary and sufficient condition on a minimal subshift to allow for a uniform subadditive ergodic theorem. This provides in par...

We study the problem of allocating heterogeneous indivisible tasks in a multi-object-demand model (i.e., each agent can be assigned multiple objects) where monetary transfers are allowed. Agents’ costs for performing tasks are their private information and depend on what other tasks they are obtained with. First, we show that when costs are unrestricted or superadditive, then there is no envy-f...

1 Subadditive Valuations 1.1 The Setup In this lecture we study a scenario that generalizes almost all of the ones that we've studied in the course. • A set U of m non-identical items. As always, we also assume that every valuation satisfies v i (∅) = 0 and is monotone (i.e., S ⊆ T implies v i (S) ≤ v(T)). Subadditivity is yet another way to formalize the idea that items are not complements — t...

We analyze a separation procedure for Mixed-Integer Programs related to the work of Gomory and Johnson on interpolated subadditive functions. This approach has its roots in the Gomory-Johnson characterization on the master cyclic group polyhedron. To our knowledge, the practical benefit that can be obtained by embedding interpolated subadditive cuts in a cutting plane algorithm was not investig...

Traditional probabilistic description of uncertainty is based on additive probability measures. To describe nonprobabilistic uncertainty, it is therefore reasonable to consider non-additive measures. An important class of non-additive measures are possibility measures, for which μ(A ∪ B) = max(μ(A), μ(B)). In this paper, we show that possibility measures are, in some sense, universal approximat...

We explore the consequences of assuming that bounded space-time subsets contain a finite number of degrees of freedom. A physically natural hypothesis is that this number is additive for spatially separated subsets. We show that this assumption conflicts with the Lorentz symmetry of Minkowski space since it implies that a conserved current determines the number of degrees of freedom. However, t...

We analyze how customers with limited attention value and choose among health plans. We show how the model can accommodate four observations regarding plan choice. First, people tend to overweight the premium and thus underappreciate the value of health insurance. Second, insurance companies may have a strong incentive to reduce quality and to hide these shortcomings in the ne print while attra...