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COMPUTATION OF THE PERIMETER OF MEASURABLE SETS VIA THEIR COVARIOGRAM. APPLICATIONS TO RANDOM SETS

COMPUTATION OF THE PERIMETER OF MEASURABLE SETS VIA THEIR COVARIOGRAM. APPLICATIONS TO RANDOM SETS

The following section gathers several known results from the theory of functions of bounded directional variation. In Section “Directional variation, perimeter and covariogram of measurable sets”, the main results relating both the derivative at the origin and the Lipschitz continuity of the covariogram of a set to its directional variations and its perimeter are stated. Finally, in the last section, applications of these results to the theory of random closed sets are discussed and illustrated.

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Finitely subadditive outer measures, finitely superadditive inner measures and their measurable sets

Finitely subadditive outer measures, finitely superadditive inner measures and their measurable sets

These considerations lead us to a general analysis of finitely subadditive outer measures on PX and finitely superadditive inner measures on 7X [For a finite outer measure countably suba[r]

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Measurable circle squaring

Measurable circle squaring

menting paths of length at most 2i + 1 in an arbitrary measurable way until none remains. This works by the observation of Lyons and Nazarov [25, Re- mark 2.6] that (13) and (14) are satisfied automatically provided G has the expansion property (i.e. there is ε > 0 such that the measure of the neighbour- hood of X is at least (1 +ε)λ(X) for every set X occupying at most half of one part in measure). As shown in [10], the expansion property applies to a wide range of pairs A, B. For example, one of the results in [10] is that two bounded Lebesgue measurable sets A, B ⊆ R k for k > 3 are measurably equidecompos-
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Measurable circle squaring

Measurable circle squaring

menting paths of length at most 2i + 1 in an arbitrary measurable way until none remains. This works by the observation of Lyons and Nazarov [25, Re- mark 2.6] that (13) and (14) are satisfied automatically provided G has the expansion property (i.e. there is ε > 0 such that the measure of the neighbour- hood of X is at least (1 +ε)λ(X) for every set X occupying at most half of one part in measure). As shown in [10], the expansion property applies to a wide range of pairs A, B. For example, one of the results in [10] is that two bounded Lebesgue measurable sets A, B ⊆ R k for k > 3 are measurably equidecompos-
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Vol 3, No 4 (2012)

Vol 3, No 4 (2012)

In section 2, based on Tanaka (2009) [7], the fundamentals of lattice sigma algebra, lattice measure on a lattice sigma algebra were described. Further based on Anil kumar etrl (2011) [2] the concepts of lattice measurable set, lattice measure space and lattice σ – finite measure were defined. Here some elementary properties of lattice measurable sets were derived.

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Outer measures, measurability, and lattice regular measures

Outer measures, measurability, and lattice regular measures

the interplay between the measurable sets associated with these outer measures, regularity properties of the measures, smoothness properties of the measures, and lattice topological prop[r]

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Perceiving 3D in the absence of measurable stereo-acuity

Perceiving 3D in the absence of measurable stereo-acuity

At present there is no conclusive explanation of 3D perception in the absence of measurable stereo-acuity. However, we observe three key differences between 3D entertainment media and clinical stereotests. First, the artistic/monocular/pictorial cues in the image can cause monocular stereopsis, the illusion of depth from a flat image. Second, moving images provide additional monocular and stereoscopic motion cues. Third, the 3D display technology itself, the methods of 3D presenta- tion, generate both supraliminal and subliminal artefacts. Depth can be identified through a number of pictorial cues such as linear perspective, relative size, texture gradient, height in the visual field, aerial perspective (blur), occlusion, lighting and shadow. 16 While pictorial
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More on vague sets

More on vague sets

Attanassov, K.T., Gargov, G. 1989. Interval valued intuitionstics fuzzy sets; Fuzzy sets and system. 343-349. Bustince, H., Buriuo, P. 1996. Vague sets are intutionistics fuzzy sets. Fuzzy sets and system 79 403-405. Dubois, D. and Prade , H. 1980. Fuzzy sets and systems : Theory and Applications, Academic press, New York. Gau, W. L., Daniel, J. B. 1993. Vague sets, IEEE transactions on systems, man Cybernetics 23 610-614. Zadeh, L.A. 1965. fuzzy sets. Information and control 8 338-353.

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Making Goals Meaningful, Measurable and Manageable

Making Goals Meaningful, Measurable and Manageable

The goals and objectives component of the IPP provides a functional, working document that a teacher can use in planning, developing, implementing and assessing programming for individual students. Goals and objectives that are meaningful, measurable and manageable allow teachers to plan, organize and deliver instruction to meet those goals and objectives, and greatly increase students’ chances of success. Meaningful, measurable and manageable goals and objectives also ensure that everyone on a student’s learning team has the same expectations for what the student will be doing over the school year, and make it easier to see and
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Measurable multifunctions and their applications to convex integral functionals

Measurable multifunctions and their applications to convex integral functionals

In this section we use the theoretical results obtained previously, to conduct a study of convex integral functlonals which are defined on Lebesgue-Bochner spaces.. dimensions and Bismut[r]

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MULTIPLICATION OPERATORS IN MEASURABLE SECTIONS SPACES

MULTIPLICATION OPERATORS IN MEASURABLE SECTIONS SPACES

For the rest of the paper, (Ω, Σ, µ) is assumed to be a finite measure space, E is a order continuous K¨ othe function space over (Ω, Σ, µ). At first we introduce the kind of measurable bundles of Banach spaces, which we need. Liftable mea- surable bundle of Banach spaces X over (Ω, Σ, µ) is said to have a Generalized M-basis or GM-basis for short if there is a family (ϕ i , ϕ ⋆ i ) i∈I measurable section,

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A Guide To Writing Measurable Goals and Objectives For

A Guide To Writing Measurable Goals and Objectives For

Through evaluation procedures and with 85 accuracy, the student will ask discerning and searching questions when gathering information. Through evaluation procedures and with 85 ac[r]

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The Impact of a Measurable Antenna in Radio
Wave Transmission

The Impact of a Measurable Antenna in Radio Wave Transmission

(b) Wave motion: Wave motion is a continuous reoccurrence of a disturbance as it travels with or without a physical medium through space e.g. the continuous disturbance we generate wh[r]

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Evaluation of Trust in the Internet Of Things: Models, Mechanisms And Applications

Evaluation of Trust in the Internet Of Things: Models, Mechanisms And Applications

The trust concept itself is a complicated notion with different meanings depending on both participants and situations and influenced by both measurable and non-measurable factors. Ther[r]

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Making Success Measurable Through Quality Control

Making Success Measurable Through Quality Control

5. Personal management, including time management, interpersonal skills, integrity, ethics. 6. Knowledge of workplace rules and requirements (e.g., worker safety, sexual harassment). Supervisory Skill Set (Supervisors and Managers of the Income and Rent Function) Note: Front-line supervisors require the skills sets identified above for rent specialists as well as the following skill sets.

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MoL 2013 12: 
  Determinacy and measurable cardinals in HOD

MoL 2013 12: Determinacy and measurable cardinals in HOD

Given the universe of set theory, V , and a set I we can define as V I the class of functions with domain I. Even though the equivalence classes modulo U are not sets but proper classes we can turn them into sets by cutting them at the least level of the cumulative hierarchy in which they are non-empty (this trick was first applied by Dana Scott and it is known as Scott’s Trick). Thus we can define V I /U as above (which is extensional because if some [f ] is cut at height

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Two variables functionals and inequalities related to measurable operators

Two variables functionals and inequalities related to measurable operators

The novelty of the proofs of Corollary 3.5 and Theorem 3.11 is applying the perspective of a one variable convex function of measurable operators. See [18] for more information and details on noncommutative perspectives. Moreover, one more perspective yields the following result, which is also a special case of Theorem 3.11.

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On Anderson–Taylor type inequalities for τ measurable operators

On Anderson–Taylor type inequalities for τ measurable operators

In this article we consider τ -measurable operators affiliated with a finite von Neumann algebra equipped with a normal faithful finite trace τ . By virtue of the method of Lin and Zhan [8, 10], based on the notion of generalized singular value studied by Fack and Kosaki [5], we obtain generalizations of results in [8] and [10] with regard to Anderson–Taylor type inequalities for τ -measurable operators case.

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A Measurable Model of the Creative Process in the Context of a Learning Process

A Measurable Model of the Creative Process in the Context of a Learning Process

We look at the process from its finalized form, that is we see a set of ingredients with a partial order (or a more general relation if wanted) covered by finite sets of aspects describing the ingredients completely (or as good as possible) with aspect relations defining in some sense (to be clarified later) the underlying relation between ingredients which are shadow objects, i.e., satisfactory approximations of some reality. We also see how this blue-print evolved in time with temporary shadow objects, temporary sets of aspects and relations; this time evolution can be encoded by giving to each component in the final picture a function of the time interval for the process to the interval of numbers between 0 and 1, expressing for example the percentage of realization of the component at that moment in time. The learning process based on the shadow objects as ingredients is thus evolving in time growing in a discrete way within the final form framework step by step realizing each final component at certain (different) moments in time.
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Determining process latitude with electrically measurable test structures

Determining process latitude with electrically measurable test structures

Once into the the computer tions between variables will the and data a second factorial full experiment composite design is operating points will The time, variables development this pla[r]

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