Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lorentzian Manifolds and Causal Sets as Partially Ordered Measure Spaces   We consider Lorentzian manifolds as examples of partially ordered measure
spaces, sets endowed with compatible partial order relations and measures, in
this case given by the causal structure and the volume element defined by each
Lorentzian metric. This places the structure normally used to describe
spacetime in geometrical theories of gravity in a more general context, which
includes the locally finite partially ordered sets of the causal set approach
to quantum gravity. We then introduce a function characterizing the closeness
between any two partially ordered measure spaces and show that, when restricted
to compact spaces satisfying a simple separability condition, it is a distance.
In particular, this provides a quantitative, covariant way of describing how
close two manifolds with Lorentzian metrics are, or how manifoldlike a causal
set is.

15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess