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Joey Lakerdas-Gayle, University of Waterloo

Dominant functions and high sets

We prove Martin's theorem that \(A'\geq_T\emptyset''\) if and only if $A$ computes a function that bounds every total computable function almost everywhere. Then we will begin discussing the infinite injury priority tree construction of Sacks' theorem that there exists a high incomplete c.e. set.

MC 5403

Julius Frizzell, University of Waterloo

Examples of Factors and Conditional expectation

We will discuss examples of factors of measure preserving systems arising from products and skew-products. We will also briefly define regular and separable extensions. We will then introduce the concept of Conditional expectation and prove some of its basic properties.

MC 5417