We give a correspondence between two notions of complexity for real numbers and functions: poly-time computability according to Ko and a notion that arises naturally when one cons...
The Denjoy-Young-Saks Theorem from classical analysis states that for an arbitrary function f : R → R, the Denjoy alternative holds outside a null set, i.e., for almost every re...
"These lecture notes treat various versions of the so-called “fundamental theorem
of asset pricing”. Many students are familiar with statements about models for
financia...
We de ne the e ective integrability of Fine-computable functions and e ectivize some fundamental limit theorems in the theory of Lebesgue integral such as Bounded Convergence Theo...
The Graph Theorem of classical recursion theory states that a total function on the natural numbers is computable, if and only if its graph is recursive. It is known that this res...