Measurable Gambling Houses

Measurable Utility and the Measurable Choice Theorem

Green houses.

We designed a web server for the analysis of biosynthetic capacities of metabolic networks. The implementation is based on the network expansion algorithm and the concept of scopes. For a given network and predefined external resources, called the seed metabolites, the scope is defined as the set of products which the network is in principle able to produce. Through the web interface the user c...

Measurable Transformations

Measurable Sensitivity

We introduce the notions of measurable and strong measurable sensitivity, which are measure-theoretic versions of the conditions of sensitive dependence on initial conditions and strong sensitive dependence on initial conditions, respectively. Strong measurable sensitivity is a consequence of light mixing, implies that a transformation has only finitely many eigenvalues, and does not exist in t...

Measurable Categories

We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a rigorous construction for the bicategory used in [4] and [3] as the basis for a representation theory of (Lie) 2-groups. Two important technical results are establishe...