Ind-additive functionals on random vectors

Wojbor A. Woyczyński

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Displaying similar documents to “Ind-additive functionals on random vectors”

Integral representation of additive transformations on $L_{p}$ spaces

Utpal Bandyopadhyay (1973)

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Decomposition of group-valued additive set functions

Tim Traynor (1972)

Annales de l'institut Fourier

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Let $m$ be an additive function on a ring $H$ of sets, with values in a commutative Hausdorff topological group, and let $K$ be an ideal of $H$ . Conditions are given under which $m$ can be represented as the sum of two additive functions, one essentially supported on $K$ , the other vanishing on $K$ . The result is used to obtain two Lebesgue-type decomposition theorems. Other applications and the corresponding theory for outer measures are also indicated.

On Vitali-Hahn-Saks-Nikodym type theorems

Barbara T. Faires (1976)

Annales de l'institut Fourier

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A Boolean algebra $𝒜$ has the interpolation property (property (I)) if given sequences $(a_{n})$ , $(b_{m})$ in $𝒜$ with $a_{n} \leq b_{m}$ for all $n, m$ , there exists an element $b$ in $𝒜$ such that $a_{n} \leq b \leq b_{n}$ for all $n$ . Let $𝒜$ denote an algebra with the property (I). It is shown that if $(μ_{n} : 𝒜 \to X)$ ( $X$ a Banach space) is a sequence of strongly additive measures such that ${lim}_{n} μ_{n} (a)$ exists for each $a \in 𝒜$ , then $μ (a) = {lim}_{n} μ_{n} (a)$ defines a strongly additive map from $𝒜$ to $X$ the $μ_{n}^{'} s$ are uniformly strongly additive. The Vitali-Hahn-Saks (VHS) theorem for strongly additive...

On a conjecture of Sárközy and Szemerédi

Yong-Gao Chen (2015)

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Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. In 1994, Sárközy and Szemerédi conjectured that there exist infinite additive complements A and B with lim sup A(x)B(x)/x ≤ 1 and A(x)B(x)-x = O(minA(x),B(x)), where A(x) and B(x) are the counting functions of A and B, respectively. We prove that, for infinite additive complements A and B, if lim sup A(x)B(x)/x ≤ 1, then, for any given...

Why $λ$ -additive (fuzzy) measures?

Ion Chiţescu (2015)

Kybernetika

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The paper is concerned with generalized (i. e. monotone and possibly non-additive) measures. A discussion concerning the classification of these measures, according to the type and amount of non-additivity, is done. It is proved that $λ$ -additive measures appear naturally as solutions of functional equations generated by the idea of (possible) non additivity.

On the concentration of certain additive functions

Dimitris Koukoulopoulos (2014)

Acta Arithmetica

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We study the concentration of the distribution of an additive function f when the sequence of prime values of f decays fast and has good spacing properties. In particular, we prove a conjecture by Erdős and Kátai on the concentration of $f (n) = \sum_{p | n} {(l o g p)}^{- c}$ when c > 1.

Unique factorisation of additive induced-hereditary properties

Alastair Farrugia, R. Bruce Richter (2004)

Discussiones Mathematicae Graph Theory

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An additive hereditary graph property is a set of graphs, closed under isomorphism and under taking subgraphs and disjoint unions. Let ₁,...,ₙ be additive hereditary graph properties. A graph G has property (₁∘...∘ₙ) if there is a partition (V₁,...,Vₙ) of V(G) into n sets such that, for all i, the induced subgraph $G [V_{i}]$ is in $_{i}$ . A property is reducible if there are properties , such that = ∘ ; otherwise it is irreducible. Mihók, Semanišin and Vasky [8] gave a factorisation for any additive...

A theorem in additive number theory

Roger Crocker (1969)

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On additive functions with a non-decreasing normal order

W. Narkiewicz (1974)

Colloquium Mathematicae

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On additive functions having a non-decreasing normal order

I. Kátai (1977)

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On Meager Additive and Null Additive Sets in the Cantor Space $2^{ω}$ and in ℝ

Tomasz Weiss (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let T be the standard Cantor-Lebesgue function that maps the Cantor space $2^{ω}$ onto the unit interval ⟨0,1⟩. We prove within ZFC that for every $X \subseteq 2^{ω}$ , X is meager additive in $2^{ω}$ iff T(X) is meager additive in ⟨0,1⟩. As a consequence, we deduce that the cartesian product of meager additive sets in ℝ remains meager additive in ℝ × ℝ. In this note, we also study the relationship between null additive sets in $2^{ω}$ and ℝ.