  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.
