Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Axiomatizing Resource Bounds for Measure   Resource-bounded measure is a generalization of classical Lebesgue measure
that is useful in computational complexity. The central parameter of
resource-bounded measure is the {\it resource bound} $\Delta$, which is a class
of functions. When $\Delta$ is unrestricted, i.e., contains all functions with
the specified domains and codomains, resource-bounded measure coincides with
classical Lebesgue measure. On the other hand, when $\Delta$ contains functions
satisfying some complexity constraint, resource-bounded measure imposes
internal measure structure on a corresponding complexity class.
  Most applications of resource-bounded measure use only the
"measure-zero/measure-one fragment" of the theory. For this fragment, $\Delta$
can be taken to be a class of type-one functions (e.g., from strings to
rationals). However, in the full theory of resource-bounded measurability and
measure, the resource bound $\Delta$ also contains type-two functionals. To
date, both the full theory and its zero-one fragment have been developed in
terms of a list of example resource bounds chosen for their apparent utility.
  This paper replaces this list-of-examples approach with a careful
investigation of the conditions that suffice for a class $\Delta$ to be a
resource bound. Our main theorem says that every class $\Delta$ that has the
closure properties of Mehlhorn's basic feasible functionals is a resource bound
for measure.
  We also prove that the type-2 versions of the time and space hierarchies that
have been extensively used in resource-bounded measure have these closure
properties. In the course of doing this, we prove theorems establishing that
these time and space resource bounds are all robust.

18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex