scholarly journals A Riesz type integral representation theorem of comonotonically additive functionals

2011 ◽  
Vol 23 (4) ◽  
pp. 592-595
Author(s):  
Jun KAWABE ◽  
Tadahiro SOMA
Keyword(s):  
Integral Representation ◽  
Representation Theorem ◽  
Additive Functionals ◽  
Type Integral

Additive Functionals on Lp Spaces

1966 ◽  
Vol 18 ◽  
pp. 1264-1271 ◽  
Author(s):  
N. Friedman ◽  
M. Katz
Keyword(s):  
Metric Space ◽  
Representation Theorem ◽  
Compact Metric Space ◽  
Lp Spaces ◽  
Additive Functionals ◽  
Measurable Functions ◽  
Present Purpose

In (1) a representation theorem was proved for a class of additive functionals defined on the continuous real-valued functions with domain S = [0, 1]. The theorem was extended to the case where S is an arbitrary compact metric space in (3). Our present purpose is to consider the corresponding class of additive functionals defined on Lp spaces, p > 0. In (4) Martin and Mizel have considered functionals defined on the class of bounded measurable functions which, however, satisfy a certain “stochastic” condition which we do not require.

scholarly journals Linear operators on Köthe spaces of vector fields

2013 ◽  
Vol 21 (2) ◽  
pp. 53-80
Author(s):  
Ion Chiţescu ◽  
Liliana Sireţchi
Keyword(s):  
Integral Representation ◽  
Representation Theorem ◽  
Vector Fields ◽  
Linear Operators ◽  
Köthe Spaces

Abstract The study of Köthe spaces of vector fields was initiated by the present authors. In this paper linear operators on these spaces are studied. An integral representation theorem is given and special types of linear operators are introduced and studied.

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