A decomposition theorem for Banach space valued fuzzy Henstock integral

2015 ◽  
Vol 259 ◽  
pp. 21-28 ◽  
Author(s):  
Kazimierz Musiał
Keyword(s):  
Banach Space ◽  
Decomposition Theorem ◽  
Henstock Integral

A decomposition theorem for the fuzzy Henstock integral

2012 ◽  
Vol 200 ◽  
pp. 36-47 ◽  
Author(s):  
B. Bongiorno ◽  
L. Di Piazza ◽  
K. Musiał
Keyword(s):  
Decomposition Theorem ◽  
Henstock Integral

A Decomposition Theorem for Compact-Valued Henstock Integral

2006 ◽  
Vol 148 (2) ◽  
pp. 119-126 ◽  
Author(s):  
L. Di Piazza ◽  
K. Musiał
Keyword(s):  
Decomposition Theorem ◽  
Henstock Integral

DECOMPOSITIONS OF SPACES OF MEASURES

2008 ◽  
Vol 11 (01) ◽  
pp. 119-126
Author(s):  
IOANNIS ANTONIOU ◽  
COSTAS KARANIKAS ◽  
STANISLAV SHKARIN
Keyword(s):  
Banach Space ◽  
Absolute Continuity ◽  
Linear Subspace ◽  
Decomposition Theorem ◽  
Measurable Space ◽  
Jordan Decomposition ◽  
Closed Linear Subspace ◽  
Complex Valued ◽  
Spaces Of Measures ◽  
Nikodym Theorem

Let 𝔐 be the Banach space of σ-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of 𝔐 is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon–Nikodým theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen–Wintner purity theorem for our decompositions.

Decay measures on locally compact abelian topological groups

2001 ◽  
Vol 131 (6) ◽  
pp. 1257-1273 ◽  
Author(s):  
I. Antoniou ◽  
S. A. Shkarin
Keyword(s):  
Banach Space ◽  
Decomposition Theorem ◽  
Topological Groups ◽  
Locally Compact ◽  
Topological Abelian Group ◽  
Absolutely Continuous ◽  
Borel Set ◽  
Direct Sum ◽  
Continuous Measures ◽  
Complex Valued

We show that the Banach space M of regular σ-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces MD and MND, where MD is the set of measures μ ∈ M whose Fourier transform vanishes at infinity and MND is the set of measures μ ∈ M such that ν ∉ MD for any ν ∈ M {0} absolutely continuous with respect to the variation |μ|. For any corresponding decomposition μ = μD + μND (μD ∈ MD and μND ∈ MND) there exist a Borel set A = A(μ) such that μD is the restriction of μ to A, therefore the measures μD and μND are singular with respect to each other. The measures μD and μND are real if μ is real and positive if μ is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from MD and MND.

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