Computing the exponent of a Lebesgue space

Timothy McNicholl


We consider the question as to whether the exponent of a computably presentable Lebesgue space whose dimension is at least 2 must be computable.  We show this very natural conjecture is true when the exponent is at least 2 or when the space is finite-dimensional.  However, we also show there is no uniform solution even when given upper and lower bounds on the exponent.  The proof of this result leads to some basic results on the effective theory of stable random variables.  


computable analysis, computable structure theory, computable probability theory, functional analysis

Full Text:

7. [PDF]


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

Journal of Logic and Analysis ISSN:  1759-9008