Masters Project Defense: “Prevalence as a definition of genericity and the Hausdorff dimensions of continuous functions” | Department of Mathematics
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Masters Project Defense: “Prevalence as a definition of genericity and the Hausdorff dimensions of continuous functions”

Event Information
Speaker: 
Ben Schwaighofer
Event Location: 
GAB 461
Event Date: 
Tuesday, July 1, 2014 - 3:00pm

Professor Pieter Allaart invites you to attend the Masters project defense of Ben Schwaighofer next Tuesday, July 1st at 3:00 pm in GAB 461. Cookies and coffee will be served in GAB 472 following this event.

"Prevalence as a definition of genericity and the Hausdorff dimensions of continuous functions"

Abstract:

There exist varying definitions of a subset being 'generic' which could be used to determine the Hausdorff dimension of a generic function in C[0, 1]. In this talk we first examine the usefulness of the Baire Category definition, then follow the development of prevalence as a preferable method from a measure theoretic standpoint. We also examine Fraser and Hyde's proof that a prevalent continuous function has Hausdorff dimension 2.