We study several properties of the Banach lattices L p (m) and L p w (m) of p-integrable scalar functions and weakly p-integrable scalar functions with respect to a countably additive vector measure m. The relation between these two spaces plays a fundamental role in our analysis.
Mathematics Subject Classification 2000: 46G10, 46E30
Study design: Cross-sectional validation study. Objectives: The goals of this study were to validate the use of accelerometers by means of multiple linear models (MLMs) to estimate the O 2 consumption (VO 2 ) in paraplegic persons and to determine the best placement for accelerometers on the human body. Setting: Non-hospitalized paraplegics' community. Methods: Twenty participants (age ¼ 40.03 years, weight ¼ 75.8 kg and height ¼ 1.76 m) completed sedentary, propulsion and housework activities for 10 min each. A portable gas analyzer was used to record VO 2 . Additionally, four accelerometers (placed on the non-dominant chest, non-dominant waist and both wrists) were used to collect second-by-second acceleration signals. Minute-byminute VO 2 (ml kg À1 min À1 ) collected from minutes 4 to 7 was used as the dependent variable. Thirty-six features extracted from the acceleration signals were used as independent variables. These variables were, for each axis including the resultant vector, the percentiles 10th, 25th, 50th, 75th and 90th; the autocorrelation with lag of 1 s and three variables extracted from wavelet analysis. The independent variables that were determined to be statistically significant using the forward stepwise method were subsequently analyzed using MLMs. Results: The model obtained for the non-dominant wrist was the most accurate (VO 2 ¼ 4.0558 À0.0318Y 25 þ 0.0107Y 90 þ 0.0051 Y ND2 À0.0061Z ND2 þ 0.0357VR 50 ) with an r-value of 0.86 and a root mean square error of 2.23 ml kg À1 min À1 . Conclusions: The use of MLMs is appropriate to estimate VO 2 by accelerometer data in paraplegic persons. The model obtained to the non-dominant wrist accelerometer (best placement) data improves the previous models for this population.
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