scholarly journals Vector measure Maurey–Rosenthal-type factorizations and ℓ-sums of L1-spaces

2005 ◽  
Vol 220 (2) ◽  
pp. 460-485 ◽  
Author(s):  
A. Fernández ◽  
F. Mayoral ◽  
F. Naranjo ◽  
C. Sáez ◽  
E.A. Sánchez-Pérez
Keyword(s):  
Vector Measure

Compression evaluation of surgery video recordings retaining diagnostic credibility (compression evaluation of surgery video)

2008 ◽  
Vol 16 (4) ◽  
Author(s):  
M. Duplaga ◽  
M. Leszczuk ◽  
Z. Papir ◽  
A. Przelaskowski
Keyword(s):  
Digital Video ◽  
Vector Measure ◽  
Lossless Compression ◽  
Video Content ◽  
Video Recordings ◽  
Subjective Tests ◽  
Objective Tests ◽  
Correlated Factors ◽  
Sort Algorithm

AbstractWider dissemination of medical digital video libraries is affected by two correlated factors, resource effective content compression that directly influences its diagnostic credibility. It has been proved that it is possible to meet these contradictory requirements halfway for long-lasting and low motion surgery recordings at compression ratios close to 100 (bronchoscopic procedures were a case study investigated). As the main supporting assumption, it has been accepted that the content can be compressed as far as clinicians are not able to sense a loss of video diagnostic fidelity (a visually lossless compression).Different market codecs were inspected by means of the combined subjective and objective tests toward their usability in medical video libraries. Subjective tests involved a panel of clinicians who had to classify compressed bronchoscopic video content according to its quality under the bubble sort algorithm. For objective tests, two metrics (hybrid vector measure and hosaka Plots) were calculated frame by frame and averaged over a whole sequence.

scholarly journals Rybakov's theorem in Fréchet spaces and completeness of L1-spaces

1998 ◽  
Vol 64 (2) ◽  
pp. 247-252 ◽  
Author(s):  
W. J. Ricker
Keyword(s):  
Sequence Space ◽  
Vector Measure ◽  
Direct Proof ◽  
Fréchet Spaces

AbstractWe provide a simple and direct proof of the completeness of the L1-space of any vector measure taking its values in the class of Fréchet spaces which do not contain a copy of the sequence space ω.

Summability in L1 of a vector measure

2016 ◽  
Vol 290 (4) ◽  
pp. 507-519 ◽  
Author(s):  
J. M. Calabuig ◽  
J. Rodríguez ◽  
E. A. Sánchez-Pérez
Keyword(s):  
Vector Measure

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].

scholarly journals Spaces of integrable functions with respect to a vector measure and factorizations through Lp and Hilbert spaces

2007 ◽  
Vol 330 (2) ◽  
pp. 1249-1263 ◽  
Author(s):  
A. Fernández ◽  
F. Mayoral ◽  
F. Naranjo ◽  
C. Sáez ◽  
E.A. Sánchez-Pérez
Keyword(s):  
Hilbert Spaces ◽  
Vector Measure ◽  
Integrable Functions
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