NONCOMMUTATIVE VERSIONS OF PROHOROV AND VARADHAN THEOREMS

Abstract

In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).In [7], we introduced a notion of capacities on a C*-algebra U, endowed the set of capacities with the narrow and vague topologies, and studied relative compactness in various classes of capacities. This allowed us to formulate a large deviation principle for a net of capacities in terms of convergence of capacities (extending the usual definition for a net (? ?)> ?>0 of regular probability measures on a locally compact Hausdorff space X).