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Titlebook: Encyclopedia of Distances; Michel Marie Deza,Elena Deza Book 20132nd edition Springer-Verlag Berlin Heidelberg 2013 distance.metric space.

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Introduction and Literature Overview, . arose as the field of knowledge dealing with spatial relationships. It was one of the two fields of pre-modern Mathematics, the other being the study of numbers.
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Tomislav Jemriić,Nikola PavičićA . is a real two-dimensional . . ., i.e., a ., each point of which has a neighborhood which is homeomorphic to a plane ., or a closed half-plane (cf. Chap. .).
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S. del Valle-Tascon,J. L. Carrasco-RodriguezA . (.,⋅,.) is a set . of elements with a binary operation ⋅, called the ., that together satisfy the four fundamental properties of . (.⋅.∈. for any .,.∈.), . (.⋅(.⋅.)=(.⋅.)⋅. for any .,.,.∈.), the . (.⋅.=.⋅.=. for any .∈.), and the . (for any .∈., there exists an element . .∈. such that .⋅. .=. .⋅.=.).
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Transient Behavior of Bernoulli LinesA . is a . ., where . is the set of all measurable subsets of ., and . is a measure on . with .(.)=1. The set . is called a .. An element . is called an .. In particular, an . is a subset of . that contains only one element. .(.) is called the . of the event .. The measure . on . is called a ., or (.) ., or simply (.) ..
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General DefinitionsLet . be a set. A function .:.×.→ℝ is called a . (or .) on . if, for all .,.∈., there holds:
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