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Spaces of measurable functions
measurable functions absolute retracts infinite-dimensional manifolds reflective isotopy property Z-sets
2011/8/29
Abstract: For a metrizable space $X$ and a finite measure space $(\Omega,\mathfrak{M},\mu)$ let $M_{\mu}(X)$ and $M^f_{\mu}(X)$ be the spaces of all equivalence classes (under the relation of equality...
An Inequality for Correlated Measurable Functions
Integral inequalities Measure Cartesian product Ordered set
2008/7/2
A classical inequality, which is known for families of monotone functions, is generalized to a larger class of families of measurable functions. Moreover we characterize all the families of functions ...
Vector Spaces of Non-measurable Functions
lineability spaceability non-measurable functions density character
2007/12/10
We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimensio...
Some Applications of the Lattice Finite Representability in Spaces of Measurable Functions
Integral operators Ultraproducts of spaces and maps
2010/3/1
We study the lattice finite representability of the Bochner space Lp(m1,Lq(m2)) in \ellp{\ellq}, 1 \le p,q < \infty, and then we characterize the ideal of the operators which factor through a lattice ...