Geodesic
Results in Q-measure
Mathematica Applicanda, Tome 50 (2022) no. 2, pp. 183-215.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

This paper introduces the notion of a generalized measure for a sequence of functions with oscillation and concentration effects. This measure is constructed by averaging the sequence of Borel measurable functions using singular or regular perturbations. In this way, the generalized limits of such sequences are conceptualized by enlarging the space of functions to measure spaces. It is a modification of the Young measure. This modified measure was termed a Q-measure. It can be difficult to determine the Young measure for a broad function. The Q-measure can be easily calculated for particular functions. This is one of the advantages of this study. As an application of the measure, we can define another weaker type of Monotone convergence theorem, the Lebesgue-dominated convergent theorem. A notion of average for underlying sequences to define the Q-measure is given, as also its application in signal analysis and atmospheric sciences.
DOI : 10.14708/ma.v50i2.7150
Classification : 60A10, 65K10, 49J20, 97N40, 60B10
Mots-clés : Young measure, Atmospheric boundary layer, Borel measurable functions, Weak* limit, Empirical Mode Decomposition. 
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C. R. Jisha. Results in Q-measure. Mathematica Applicanda, Tome 50 (2022) no. 2, pp.  183-215. doi : 10.14708/ma.v50i2.7150. http://geodesic.mathdoc.fr/articles/10.14708/ma.v50i2.7150/

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