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A Stone's Representation Theorem and Some Applications
Habil, Eissa D. (The Scientific and Technological Research Council of Turkey, 2000)In this paper, we prove the following form of Stone's representation theorem: Let\sum be a\sigmaalgebra of subsets of a set X. Then there exists a totally disconnected compact Hausdorff space {\cal K} for which (\sum,\cup,\cap) ... 
BrooksJewett and Nikodym convergence theorems for orthoalgebras that have the weak subsequential interpolation property
Habil, Eissa D. (Kluwer Academic PublishersPlenum Publishers, 1995)A weak form of σorthocompleteness or σorthosummability, referred to as the Weak Subsequential Interpolation Property, is defined for Orthoalgebras. It is shown that the class of Orthoalgebras that have this property ... 
Connectedness in isotonic spaces
Habil, Eissa D.; Elzenati, Khalid A. (The Scientific and Technological Research Council of Turkey, 2006)An isotonic space (X, cl) is a set X with isotonic operator cl: P (X)\to P (X) which satisfies cl (\emptyset)=\emptyset and cl (A)\subseteq cl (B) whenever A\subseteq B\subseteq X. Many properties which hold in topological ... 
Decomposition of measures on Difference posets
Habil, Eissa D.; Radwan, Akram M. (الجامعة الإسلامية  غزة, 2002)Decomposition of measures on Difference posets 
Direct limits of effect algebras
Habil, Eissa D. (Kluwer Academic PublishersPlenum Publishers, 2000)In this paper, we prove that direct limits exist in the category of effect algebrasand effect algebramorphisms. Then, as a consequence, we obtain similar knownresults for the categories of orthomodular posets and orthomodular ... 
Double Sequences and Double Series
Habil, Eissa D. (الجامعة الإسلامية  غزة, 2006)This research considers two traditional important questions, which are interesting, at least to most mathematicians. The first question arises in the theory of double sequences of complex numbers, which concerns the ... 
Hereditary Properties in Isotonic Spaces
Habil, Eissa D. (2009)An isotonic space (X, cl) is a set X with isotonic operator cl: 乡 (X)→ 
Integration with respect to a noncontinuous measure
Habil, Eissa D.; Mahdi, Hisham B. (الجامعة الإسلامية  غزة, 2002)Integration with respect to a noncontinuous measure 
Morphisms and pasting of orthoalgebras
Habil, Eissa D. (Mathematical Institute of the Slovak Academy of Sciences, 1997)We study orthoalgebra morphisms, we show how orthoalgebra monomorphisms and epimorphisms ought to be defined, and we show how orthoalgebras may be" pasted" together to yield new orthoalgebras. 
NIKODYMVITALI – HAHN – SAKS THEOREM ON AN EFFECT ALGEBRA
Habil, Eissa D. (الجامعة الإسلامية  غزة, 2004)NIKODYMVITALI – HAHN – SAKS THEOREM ON AN EFFECT ALGEBRA 
NIKODYMVITALI–HAHN–SAKS THEOREM ON AN EFFECT ALGEBRA
Habil, Eissa D. (2015)The PDF file you selected should load here if your Web browser has a PDF reader plugin installed (for example, a recent version of Adobe Acrobat Reader) … If you would like more information about how to print, save, and ... 
Nonstandard Topology on R
Habil, Eissa D.; Ghneim, Ahmed A. (الجامعة الإسلامية  غزة, 2015)Nonstandard topology on is a kind of topology constructed by means of nonstandard analysis on . The ordered field of nonstandard real numbers (or simply hyperreals) has been introduced. It extends the reals . The hyperreals ... 
On fuzzy probability theory
Habil, Eissa D.; Nasr, Taghreed Z (Kluwer Academic PublishersPlenum Publishers, 2002)Our main aim from this work is to see which theorems in classical probability theory are still valid in fuzzy probability theory. Following Gudder's approach [Demonestratio Mathematica 31(3), 1998, 235–254; Foundations of ... 
Orthoalgebras and Noncommutative Measure Theory.
Habil, Eissa D. (1993)Notions of orthosummability and sigmaorthosummability are defined for orthoalgebras. It is shown that these notions extend the known notions of orthocompleteness and sigmaorthocompleteness for orthomodular posets and ... 
Orthosummable orthoalgebras
Habil, Eissa D. (Kluwer Academic PublishersPlenum Publishers, 1994)We introduce notions of orthosummability andσorthosummability for orthoalgebras, which generalize the notions of orthocompleteness andσorthocompleteness for orthomodular posets, and we characterize such orthoalgebras in ... 
Tensor product of distributive sequential effect algebras and product effect algebras
Habil, Eissa D. (Springer US, 2008)A distributive sequential effect algebra (DSEA) is an effect algebra on which a distributive sequential product with natural properties is defined. We define the tensor product of two arbitrary DSEA’s and we give a necessary ... 
The BrooksJewett theorem for triangular functions on difference posets and orthoalgebras
Habil, Eissa D. (Mathematical Institute of the Slovak Academy of Sciences, 1997)We introduce ktriangular functions on difference posets and we prove a BrooksJewetttype theorem for such functions that are defined on a difference poset (or an effect algebra) satisfying the weak subsequential interpolation ... 
THE BROOKSJEWETT THEOREM ON AN EFFECT ALGEBRA
Habil, Eissa D. (الجامعة الإسلامية  غزة, 2003)THE BROOKSJEWETT THEOREM ON AN EFFECT ALGEBRA 
The intersection operation in light of joint observables and Bell inequalities in operational probability theory
Habil, Eissa D.; Nasr, Taghreed Z (NorthHolland, 2011)Operational probability theory appears as a smooth extension of classical probability theory that fulfills quantum physics needs. In this paper, we, first, explain the need to extend the concept of the intersection operation ... 
THE TWO SCOPES OF FUZZY PROBABILITY THEORY
Habil, Eissa D.; Nasr, Taghreed Z (2010)The aim of this work is to compare between what seems to be entirely different two highly developing “fuzzy probability” theories. The first theory had been developed firstly by statisticians and the other separately by ...