Some theorems on Borel-measurable functions
نویسندگان
چکیده
منابع مشابه
Duality for Borel Measurable Cost Functions
We consider the Monge-Kantorovich transport problem in an abstract measure theoretic setting. Our main result states that duality holds if c : X × Y → [0,∞) is an arbitrary Borel measurable cost function on the product of Polish spaces X,Y . In the course of the proof we show how to relate a non-optimal transport plan to the optimal transport costs via a “subsidy” function and how to identify t...
متن کاملBorel measurable functionals on measure algebras
For Φ,Ψ ∈ A′′, define 〈Φ Ψ, λ〉 = 〈Φ, Ψ · λ〉 (λ ∈ A′) , and similarly for ♦. Thus (A′′, ) and (A′′,♦) are Banach algebras each containingA as a closed subalgebra. The Banach algebra A is Arens regular if and ♦ coincide on A′′, and A is strongly Arens irregular if and ♦ coincide only on A. A subspace X of A′ is left-introverted if Φ · λ ∈ X whenever Φ ∈ A′′ and λ ∈ X . There has been a great deal...
متن کاملOn Measurable Sierpiński-zygmund Functions
It is proved that there exists a Sierpiński-Zygmund function, which is measurable with respect to a certain invariant extension of the Lebesgue measure on the real line R. Let E be a nonempty set and let f : E → R be a function. We say that f is absolutely nonmeasurable if f is nonmeasurable with respect to any nonzero σ-finite diffused (i.e., continuous) measure μ defined on a σ-algebra of sub...
متن کاملGeneralized Rings of Measurable and Continuous Functions
This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1963
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-10-2-261-266