The error of polytopal approximation with respect to the symmetric difference metric and theL p metric

2000 ◽  
Vol 117 (1) ◽  
pp. 1-28 ◽  
Author(s):  
Károly Böröczky
Keyword(s):  
Symmetric Difference ◽  
Symmetric Difference Metric ◽  
Polytopal Approximation

The problem of completeness for -mean symmetric difference metric

2000 ◽  
Vol 116 (3) ◽  
pp. 459-470 ◽  
Author(s):  
Fachao Li ◽  
Jiqing Qiu ◽  
Jianren Zhai
Keyword(s):  
Symmetric Difference ◽  
Symmetric Difference Metric

scholarly journals A theorem on connected graphs in which every edge belongs to a 1-factor

1974 ◽  
Vol 18 (4) ◽  
pp. 450-452 ◽  
Author(s):  
Charles H. C. Little
Keyword(s):  
Symmetric Difference ◽  
Connected Graphs

In this paper, we consider factor covered graphs, which are defined basically as connected graphs in which every edge belongs to a 1-factor. The main theorem is that for any two edges e and e′ of a factor covered graph, there is a cycle C passing through e and e′ such that the edge set of C is the symmetric difference of two 1-factors.

THE WIENER INDEX OF DISJUNCTION AND SYMMETRIC DIFFERENCE OF TWO GRAPHS

2021 ◽  
Vol 10 (4) ◽  
pp. 2045-2052
Author(s):  
S. Menaka ◽  
R.S. Manikandan ◽  
R. Muruganandam
Keyword(s):  
Wiener Index ◽  
Symmetric Difference

scholarly journals Separability of the L1-space of a vector measure

1992 ◽  
Vol 34 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Werner J. Ricker
Keyword(s):  
Banach Space ◽  
Metric Space ◽  
Classical Result ◽  
Vector Measure ◽  
Symmetric Difference ◽  
Outer Measure ◽  
Additive Measure ◽  
Image Position

Let Σ be a σ-algebra of subsets of some set Ω and let μ:Σ→[0,∞] be a σ-additive measure. If Σ(μ) denotes the set of all elements of Σ with finite μ-measure (where sets equal μ-a.e. are identified in the usual way), then a metric d can be defined in Σ(μ) by the formulahere E ΔF = (E\F) ∪ (F\E) denotes the symmetric difference of E and F. The measure μ is called separable whenever the metric space (Σ(μ), d) is separable. It is a classical result that μ is separable if and only if the Banach space L1(μ), is separable [8, p.137]. To exhibit non-separable measures is not a problem; see [8, p. 70], for example. If Σ happens to be the σ-algebra of μ-measurable sets constructed (via outer-measure μ*) by extending μ defined originally on merely a semi-ring of sets Γ ⊆ Σ, then it is also classical that the countability of Γ guarantees the separability of μ and hence, also of L1(μ), [8, p. 69].

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