scholarly journals Lebesgue Decomposition Theorem and Weak Radon-Nikodým Theorem for Generalized Fuzzy Number Measures

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Cai-Li Zhou ◽  
Fu-Gui Shi
Keyword(s):  
Banach Spaces ◽  
Fuzzy Number ◽  
Decomposition Theorem ◽  
Lebesgue Decomposition ◽  
Generalized Fuzzy Number ◽  
Lebesgue Type Decomposition ◽  
Nikodym Theorem ◽  
Type Decomposition

The Lebesgue type decomposition theorem and weak Radon-Nikodým theorem for fuzzy valued measures in separable Banach spaces are established.

scholarly journals LEBESGUE DECOMPOSITION FOR REPRESENTABLE FUNCTIONALS ON *-ALGEBRAS

2015 ◽  
Vol 58 (2) ◽  
pp. 491-501 ◽  
Author(s):  
ZSIGMOND TARCSAY
Keyword(s):  
Decomposition Theorem ◽  
Lebesgue Decomposition ◽  
Absolutely Continuous ◽  
Hermitian Forms ◽  
Lebesgue Type Decomposition ◽  
Representable Functional ◽  
Type Decomposition

AbstractWe offer a Lebesgue-type decomposition of a representable functional on a *-algebra into absolutely continuous and singular parts with respect to another. Such a result was proved by Zs. Szűcs due to a general Lebesgue decomposition theorem of S. Hassi, H.S.V. de Snoo, and Z. Sebestyén concerning non-negative Hermitian forms. In this paper, we provide a self-contained proof of Szűcs' result and in addition we prove that the corresponding absolutely continuous parts are absolutely continuous with respect to each other.

scholarly journals Absolute continuity, singularity and product measures

1982 ◽  
Vol 5 (4) ◽  
pp. 793-807
Author(s):  
Roy A. Johnson
Keyword(s):  
Absolute Continuity ◽  
Decomposition Theorem ◽  
Absolutely Continuous ◽  
Weakly Singular ◽  
Lebesgue Type Decomposition ◽  
Product Measures ◽  
Type Decomposition

Conditions are given under which a product of two semifinite measures is absolutely continuous or weakly singular with respect to another product of two semifinite measures. A Lebesgue type decomposition theorem is proved for certain product measures so that the resulting measures are themselves product measures.

scholarly journals A wide Perron integral

1986 ◽  
Vol 34 (2) ◽  
pp. 233-251
Author(s):  
D. N. Sarkhel
Keyword(s):  
Decomposition Theorem ◽  
Mean Value ◽  
Lebesgue Decomposition ◽  
Integration By Parts ◽  
Mean Value Theorems ◽  
Limit Process ◽  
Real Functions ◽  
Marcinkiewicz Theorem ◽  
Perron Integral ◽  
Interesting Generalization

In terms of an arbitrary limit process T, defined abstractly for real functions, we define in a novel way a T-continuous integral of Perron type, admitting mean value theorems, integration by parts and the analogue of the Marcinkiewicz theorem for the ordinary Perron integral. The integral is shown to include, as particular cases, the various known continuous, approximately continuous, cesàro-continuous, mean-continuous and proximally Cesàro-continuous integrals of Perron and Denjoy types. An interesting generalization of the classical Lebesgue decomposition theorem is also obtained.

Random fuzzy number integrals in Banach spaces

1994 ◽  
Vol 66 (1) ◽  
pp. 97-111 ◽  
Author(s):  
Xue Xiaoping ◽  
Ha Minghu ◽  
Ma Ming
Keyword(s):  
Banach Spaces ◽  
Fuzzy Number
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