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On the Condition of the Set which might be a Derived Set

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On Derived Sets

National Mathematics Magazine, 1943
Divers aspects de l'étude des applications de l'ensemble \(\mathfrak P(E)\) des parties d'un ensemble dans lui-même ou dans \(\mathfrak P(\mathfrak P(E)\), en vue de déterminer les liens existant entre les diverses topologies définies sur un ensemble (E. Hewitt [Zbl 0060.39407]), ou entre les diverses manières de définir une topologie (M. M.
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On the Lower Derivate of a Set Function

Canadian Journal of Mathematics, 1968
In (5), the following theorem was proved in a very general setting:(1) An additive set function is non-negative whenever its lower derivative is non-negative.For a continuous additive function of intervals, theorem (1) can be improved as follows:(2) A continuous additive set function is non-negative whenever its lower derivative is non-negative except,
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Derivative of Singular Set-Functions

Canadian Journal of Mathematics, 1965
The purpose of this paper is to prove that the general derivative of a completely additive singular set-function defined on certain measurable subsets of an abstract measure space is zero almost everywhere. As a corollary the celebrated Lebesgue decomposition theorem has been sharpened.This result is well known for set-functions defined on measurable ...
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On the derivatives of set functions in matrix representation

Information Sciences, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On connectedness of derivative sets

Ukrainian Mathematical Journal, 1993
Let \(D\) be a domain in \(\mathbb{R}^ p\), \(f: D\to \mathbb{R}^ 1\) a continuous real function. Denote a point \(x\in D\) by \((x_ 1,\dots,x_ i,\dots,x_ p)= (x_ i,y)\). A number \(d\) is called a partial derivative number (with respect to \(x_ i\)) of \(f\) at the point \(x\) if there exists a sequence of real numbers \(\{h_ n\}\), \(h_ n\to 0\), for
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