Decomposition of Lebesgue Spaces
Copyright policy )Decomposition of Lebesgue Spaces
The author proves existence and uniqueness of a canonical system of measures for a strictly separable \(\sigma\)-subalgebra of a Lebesgue space. Moreover, the product structure of the factor space for the smallest \(\sigma\)-subalgebra generated by strictly separable \(\sigma\)-subalgebras of a Lebesgue space being stochastically independent is studied. The main result concerns a complete description of all possible structures of the factor spaces in connection with a pair of stochastically commuting strictly separable \(\sigma\)-subalgebras.
- Courant Institute of Mathematical Sciences United States
- New York University United States
stochastically commuting, Mathematics(all), decomposition, stochastically independent, factor space, Measures on Boolean rings, measure algebras, Set functions and measures on spaces with additional structure, Lebesgue space
stochastically commuting, Mathematics(all), decomposition, stochastically independent, factor space, Measures on Boolean rings, measure algebras, Set functions and measures on spaces with additional structure, Lebesgue space
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