1,056 research outputs found
Note on the Regularity of Nonadditive Measures
We consider the regularity for nonadditive measures.
We prove that the non-additive measures which satisfy Egoroff's theorem and have pseudometric generating property possess Radon property (strong regularity) on a complete or a locally compact, separable metric space
Representation of maxitive measures: an overview
Idempotent integration is an analogue of Lebesgue integration where
-maxitive measures replace -additive measures. In addition to
reviewing and unifying several Radon--Nikodym like theorems proven in the
literature for the idempotent integral, we also prove new results of the same
kind.Comment: 40 page
Commutative POVMs and Fuzzy Observables
In this paper we review some properties of fuzzy observables, mainly as
realized by commutative positive operator valued measures. In this context we
discuss two representation theorems for commutative positive operator valued
measures in terms of projection valued measures and describe, in some detail,
the general notion of fuzzification. We also make some related observations on
joint measurements.Comment: Contribution to the Pekka Lahti Festschrif
On the coexistence of position and momentum observables
We investigate the problem of coexistence of position and momentum
observables. We characterize those pairs of position and momentum observables
which have a joint observable
Ideal-quasi-Cauchy sequences
An ideal is a family of subsets of positive integers which
is closed under taking finite unions and subsets of its elements. A sequence
of real numbers is said to be -convergent to a real number , if
for each \; the set belongs
to . We introduce -ward compactness of a subset of , the set
of real numbers, and -ward continuity of a real function in the senses that
a subset of is -ward compact if any sequence of
points in has an -quasi-Cauchy subsequence, and a real function is
-ward continuous if it preserves -quasi-Cauchy sequences where a sequence
is called to be -quasi-Cauchy when is
-convergent to 0. We obtain results related to -ward continuity, -ward
compactness, ward continuity, ward compactness, ordinary compactness, ordinary
continuity, -ward continuity, and slowly oscillating continuity.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1005.494
General equilibrium
Unlike partial equilibrium analysis which study the equilibrium of a particular market under the clause "ceteris paribus" that revenues and prices on the other markets stay approximately unaffected, the ambition of a general equilibrium model is to analyze the simultaneous equilibrium in all markets of a competitive economy. Definition of the abstract model, some of its basic results and insights are presented. The important issues of uniqueness and local uniqueness of equilibrium are sketched ; they are the condition for a predictive power of the theory and its ability to allow for statics comparisons. Finally, we review the main extensions of the general equilibrium model. Besides the natural extensions to infinitely many commodities and to a continuum of agents, some examples show how economic theory can accommodate the main ideas in order to study some contexts which were not thought of by the initial model.Commodity space, price space, exchange economy, production economy, feasible allocations, equilibrium, quasi-equilibrium, Pareto optimum, core, edgeworth equilibrium allocutions, time and uncertainty, continuum economies, non-convexities, public goods, incomplete markets.
- …