Results 1  10
of
1,451
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
Abstract

Cited by 5350 (67 self)
 Add to MetaCart
In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Borel and Baire reducibility
 Fund. Math
"... The Borel reducibility theory of Polish equivalence relations, at least in its present form, was initiated in [FS89]. There is now an extensive literature on this topic, including fundamental work on the GlimmEffros dichotomy in ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The Borel reducibility theory of Polish equivalence relations, at least in its present form, was initiated in [FS89]. There is now an extensive literature on this topic, including fundamental work on the GlimmEffros dichotomy in
COMPACTNESS IN THE FIRST BAIRE CLASS AND BAIRE1 OPERATORS
, 2002
"... For a polish space M and a Banach space E let B1(M,E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1(M,E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in ..."
Abstract
 Add to MetaCart
For a polish space M and a Banach space E let B1(M,E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1(M,E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy
Analytic Baire spaces
"... We generalize to the nonseparable context a theorem of Levi characterizing Baire analytic spaces. This allows us to prove a jointcontinuity result for nonseparable normed groups, previously known only in the separable context. 1 ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
We generalize to the nonseparable context a theorem of Levi characterizing Baire analytic spaces. This allows us to prove a jointcontinuity result for nonseparable normed groups, previously known only in the separable context. 1
COMPACT SUBSETS OF THE FIRST BAIRE CLASS
, 1999
"... Perhaps the earliest results about pointwise compact sets of Baire class1 functions are the two selection theorems of E. Helly found in most of the standard texts on real variable (see, e.g., [Lo], [N]). These two theorems are really theorems about a particular example of a compact set of Baire cla ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
Perhaps the earliest results about pointwise compact sets of Baire class1 functions are the two selection theorems of E. Helly found in most of the standard texts on real variable (see, e.g., [Lo], [N]). These two theorems are really theorems about a particular example of a compact set of Baire
Baire reductions and good Borel reducibilities
 J. Symbolic Logic
"... Abstract. In [8] we have considered a wide class of “wellbehaved ” reducibilities for sets of reals. In this paper we continue with the study of Borel reducibilities by proving a dichotomy theorem for the degreestructures induced by good Borel reducibilities. This extends and improves the result ..."
Abstract

Cited by 12 (7 self)
 Add to MetaCart
the results of [8] allowing to deal with a larger class of notions of reduction (including, among others, the Baire class ξ functions). 1.
RANKS ON THE BAIRE CLASS ξ FUNCTIONS
"... In 1990 Kechris and Louveau developed the theory of three very natural ranks on the Baire class 1 functions. A rank is a function assigning countable ordinals to certain objects, typically measuring their complexity. We extend this theory to the case of Baire class ξ functions, and generalize most ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In 1990 Kechris and Louveau developed the theory of three very natural ranks on the Baire class 1 functions. A rank is a function assigning countable ordinals to certain objects, typically measuring their complexity. We extend this theory to the case of Baire class ξ functions, and generalize
FURTHER BAIRE RESULTS ON THE DISTRIBUTION OF SUBSEQUENCES
, 2007
"... Dedicated to Professor Robert F. Tichy on the occasion of his 50th birthday Abstract. This paper presents results about the distribution of subsequences which are typical in the sense of Baire categories. The first main part is concerned with sequences of the type xk = nkα, n1 < n2 < n3 < · ..."
Abstract
 Add to MetaCart
Dedicated to Professor Robert F. Tichy on the occasion of his 50th birthday Abstract. This paper presents results about the distribution of subsequences which are typical in the sense of Baire categories. The first main part is concerned with sequences of the type xk = nkα, n1 < n2 < n3 <
Results 1  10
of
1,451