Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measures induced by units   The half-open real unit interval (0,1] is closed under the ordinary
multiplication and its residuum. The corresponding infinite-valued
propositional logic has as its equivalent algebraic semantics the equational
class of cancellative hoops. Fixing a strong unit in a cancellative hoop
-equivalently, in the enveloping lattice-ordered abelian group- amounts to
fixing a gauge scale for falsity. In this paper we show that any strong unit in
a finitely presented cancellative hoop H induces naturally (i.e., in a
representation-independent way) an automorphism-invariant positive normalized
linear functional on H. Since H is representable as a uniformly dense set of
continuous functions on its maximal spectrum, such functionals -in this context
usually called states- amount to automorphism-invariant finite Borel measures
on the spectrum. Different choices for the unit may be algebraically unrelated
(e.g., they may lie in different orbits under the automorphism group of H), but
our second main result shows that the corresponding measures are always
absolutely continuous w.r.t. each other, and provides an explicit expression
for the reciprocal density.

4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org