The separation from a vector measure of the part representable by a Bochner integral

1975 ◽  
Vol 17 (5) ◽  
pp. 476-482 ◽  
Author(s):  
V. I. Rybakov
Keyword(s):  
Vector Measure ◽  
Bochner Integral

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 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

scholarly journals An integral for a banach valued function

2009 ◽  
Vol 44 (1) ◽  
pp. 105-113
Author(s):  
Giuseppa Riccobono
Keyword(s):  
Banach Space ◽  
Bochner Integral ◽  
Definition Of

Abstract Using partitions of the unity ((PU)-partition), a new definition of an integral is given for a function f : [a, b] → X, where X is a Banach space, and it is proved that this integral is equivalent to the Bochner integral.

The range of a vector measure and a Radon-Nikodym problem for the variation

1998 ◽  
Vol 70 (1) ◽  
pp. 74-82
Author(s):  
Carmen Romero-Moreno
Keyword(s):  
Vector Measure

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 Integrated Semigroups on Fréchet Spaces I: Bochner Integral, Laplace Integral and Real Representation Theorems

2019 ◽  
Vol 11 (1) ◽  
pp. 118
Author(s):  
Tiziano Granucci
Keyword(s):  
Functional Space ◽  
Fréchet Spaces ◽  
Bochner Integral ◽  
Representation Theorems ◽  
Real Representation ◽  
Integrated Semigroups ◽  
Laplace Integral ◽  
Vectorial Functions

In this articles we will study the integration of the vectorial functions in Fréchet spaces. Particularly we will introduce and we will study a new functional space and we will prove some theorems of representation.

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