Displaying similar documents to “Inserting measurable functions precisely”

Normal integrands and related classes of functions

Anna Kucia, Andrzej Nowak (1995)

Commentationes Mathematicae Universitatis Carolinae

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Let D ⊂ T × X , where T is a measurable space, and X a topological space. We study inclusions between three classes of extended real-valued functions on D which are upper semicontinuous in x and satisfy some measurability conditions.

A problem with almost everywhere equality

Piotr Niemiec (2012)

Annales Polonici Mathematici

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A topological space Y is said to have (AEEP) if the following condition is satisfied: Whenever (X,) is a measurable space and f,g: X → Y are two measurable functions, then the set Δ(f,g) = x ∈ X: f(x) = g(x) is a member of . It is shown that a metrizable space Y has (AEEP) iff the cardinality of Y is not greater than 2 ℵ ₀ .

Non-autonomous implicit integral equations with discontinuous right-hand side

Giovanni Anello, Paolo Cubiotti (2004)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the implicit integral equation h ( u ( t ) ) = f ( t , ∫ I g ( t , z ) u ( z ) d z ) for a.a. t ∈ I , where I : = [ 0 , 1 ] and where f : I × [ 0 , λ ] → ℝ , g : I × I → [ 0 , + ∞ [ and h : ] 0 , + ∞ [ → ℝ . We prove an existence theorem for solutions u ∈ L s ( I ) where the contituity of f with respect to the second variable is not assumed.