Various products for Lebesgue densities

Various products for Lebesgue densities In Macheras and Strauss (Atti Sem Math Fis Univ Modena, L, pp 349–361, 2002) and Musial et al. (J Theor Probab 20:545–560, 2007) various products for primitive liftings in the factors of a product of probability spaces have been considered. In this paper we settle for the d-dimensional Lebesgue densities open problems from Macheras and Strauss (Atti Sem Math Fis Univ Modena, L, pp 349–361, 2002) and Musial et al. (J Theor Probab 20:545–560, 2007) by applying results relying on the metrical group structure of $${{\mathbb R}^d}$$ , if $${d\in{\mathbb N}}$$ . In particular, a lifting problem from Musial et al. (Arch Math 83:467–480, 2004), Question 3.3, is decided to the negative for the Lebesgue densities. The relation of the Lebesgue density in the product space and the results of the products taken for the Lebesgue densities in the factors under order is discussed. The results can be carried over to densities and liftings dominating Lebesgue densities and to multiplicative and positive linear liftings on function spaces. Positivity Springer Journals

Various products for Lebesgue densities

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SP Birkhäuser Verlag Basel
Copyright © 2010 by Springer Basel AG
Mathematics; Econometrics; Calculus of Variations and Optimal Control; Optimization; Potential Theory; Operator Theory; Fourier Analysis
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  • Existence of linear liftings with invariant sections in product measure spaces
    Musiał, K.; Strauss, W.; Macheras, N.D.

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