Notes on Measure and Category in Recursion Theory

Notes on Category Theory

Measure, Category and Learning Theory

Measure and category (or rather, their recursion theoretical counterparts) have been used in Theoretical Computer Science to make precise the intuitive notion \for most of the recursive sets." We use the notions of eeective measure and category to discuss the relative sizes of inferrible sets, and their complements. We nd that inferrible sets become large rather quickly in the standard hierarch...

M275 Notes 1.2 Category Theory

Lecture notes from M275 at SJSU, a graduate-level course at SJSU in Algebraic Topology taught by Professor Richard Kulbelka. These notes were taken using Vim and/or GVim equipped with L A T E X-Suite, which sped up typesetting significantly; latexmk with the flag-pvc was useful for compiling these notes in real-time. 1.1 The Question Question. Given two topological spaces, can we determine if t...

Lecture Notes on Measure Theory and Functional Analysis

Effective Category and Measure in Abstract Complexity Theory (Extended Abstract)

Strong variants of the Operator Speed-up Theorem, Operator Gap Theorem and Compression Theorem are obtained using an effective version of Baire Category Theorem. It is also shown that all complexity classes of recursive predicates have effective measure zero in the space of recursive predicates and, on the other hand, the class of predicates with almost everywhere complexity above an arbitrary ...