L p -Spaces and the Radon–Nikodym Theorem

2014 ◽  
pp. 145-168
Author(s):  
Achim Klenke
Keyword(s):  
Nikodym Theorem

scholarly journals A reformulation of the Radon-Nikodým theorem

1975 ◽  
Vol 47 (2) ◽  
pp. 393-393
Author(s):  
Jonathan Lewin ◽  
Mirit Lewin
Keyword(s):  
Nikodym Theorem

scholarly journals ∗-fuzzy measure model for COVID-19 disease

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abbas Ghaffari ◽  
Reza Saadati
Keyword(s):  
Mathematical Model ◽  
Fuzzy Measure ◽  
Measure Model ◽  
Nikodym Theorem

AbstractWe introduce a mathematical model, namely, ∗-fuzzy measure model for COVID-19 disease and consider some properties of ∗-fuzzy measure such as Lebesque–Radon–Nikodym theorem.

scholarly journals A Radon-Nikodym theorem in $W^*$-algebras

1965 ◽  
Vol 71 (1) ◽  
pp. 149-152 ◽  
Author(s):  
Shôichirô Sakai
Keyword(s):  
Nikodym Theorem

A SUPER RADON-NIKODYM DERIVATIVE FOR ALMOST SUBADDITIVE SET FUNCTIONS

2013 ◽  
Vol 21 (03) ◽  
pp. 347-365 ◽  
Author(s):  
YANN RÉBILLÉ
Keyword(s):  
Density Function ◽  
Measure Theory ◽  
Type Theorem ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Set Functions ◽  
Necessary And Sufficient ◽  
Exact Factorization ◽  
Nikodym Derivative ◽  
Nikodym Theorem

In classical measure theory, the Radon-Nikodym theorem states in a concise condition, namely domination, how a measure can be factorized by another (bounded) measure through a density function. Several approaches have been undertaken to see under which conditions an exact factorization can be obtained with set functions that are not σ-additive (for instance finitely additive set functions or submeasures). We provide a Radon-Nikodym type theorem with respect to a measure for almost subadditive set functions with bounded disjoint variation. The necessary and sufficient condition to guarantee a superior Radon-Nikodym derivative remains the standard domination condition for measures. We show how these set functions admit an equivalent factorization under the standard domination condition for set functions.

And Still One More Proof of the Radon-Nikodym Theorem

2003 ◽  
Vol 110 (6) ◽  
pp. 536-538 ◽  
Author(s):  
Anton R. Schep
Keyword(s):  
Nikodym Theorem

On (L1)* for General Measure Spaces

1963 ◽  
Vol 6 (2) ◽  
pp. 211-229 ◽  
Author(s):  
H. W. Ellis ◽  
D. O. Snow
Keyword(s):  
Measurable Function ◽  
Measure Space ◽  
Finite Measure ◽  
Signed Measure ◽  
General Measure ◽  
Measure Spaces ◽  
Arbitrary Measure ◽  
Image Position ◽  
Nikodym Theorem

It is well known that certain results such as the Radon-Nikodym Theorem, which are valid in totally σ -finite measure spaces, do not extend to measure spaces in which μ is not totally σ -finite. (See §2 for notation.) Given an arbitrary measure space (X, S, μ) and a signed measure ν on (X, S), then if ν ≪ μ for X, ν ≪ μ when restricted to any e ∊ Sf and the classical finite Radon-Nikodym theorem produces a measurable function ge(x), vanishing outside e, with

scholarly journals The Radon-Nikodym Theorem for Multimeasures

1978 ◽  
Vol 21 (2) ◽  
pp. 167-173
Author(s):  
Le van Tu
Keyword(s):  
Convex Space ◽  
Measurable Space ◽  
Locally Convex Space ◽  
The Family ◽  
Disjoint Sets ◽  
Locally Convex ◽  
Nikodym Theorem

Let (S, ℳ) be ameasurable space(that is, a setSin which is defined a σ-algebra ℳ of subsets) andXa locally convex space. A mapMfrom ℳ to the family of all non-empty subsets ofXis called a multimeasure iff for every sequence of disjoint setsAnɛ ℳ (n=1,2,… )withthe seriesconverges (in the sense of (6), p. 3) toM(A).

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