Results 271 to 280 of about 117,485 (309)

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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Derived sets and inductive inference

1994
The paper deals with using topological concepts in studies of the Gold paradigm of inductive inference. They are — accumulation points, derived sets of order α (α — constructive ordinal) and compactness. Identifiability of a class U of total recursive functions with a bound α on the number of mindchanges implies \(U^{(\alpha + 1)} = \not 0\).
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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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Derivatives and closed sets

Acta Mathematica Hungarica, 1984
The author proves that a real function defined on a closed set S and differentiable relative to S can be extended to a function differentiable on the whole real line. This is a generalization of a result of \textit{G. Petruska} and \textit{M. Laczkovich} [Acta. Math. Acad. Sci. Hung. 25, 189- 212 (1974; Zbl 0279.26003)].
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Weak* derived sets of sets of linear functionals

Mathematical Notes of the Academy of Sciences of the USSR, 1978
For a Banach space X the w*-sequential closure operator in the adjoint space is, in general, not the topological closure operator. That is, it may happen that the w*-sequential closure of a subspace T of X* is not w*-sequentially closed. The possible length of the chain of repeated w*-sequential closures of a subspace of X* in dependence on the ...
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Set functions and their derivatives

1996
Let S be a ring of subsets of a given set, and s a real-valued function (i.e. infinity is excluded as a value) on S. Then s is said to be of bounded (or finite) variation on a set E ∈ S, if s+(E) and S−(E) are both finite, where $${s^ + }(E) = \mathop {\sup }\limits_{\begin{array}{*{20}{l}} {F \subset E} \\ {F \in S} \end{array}} s(F),$$ and
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Uniform Continuity of Derivatives in Convex Sets

The American Mathematical Monthly, 1980
No abstract.
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Derivatives of Tree Sets with Applications to Grammatical Inference

IEEE Transactions on Pattern Analysis and Machine Intelligence, 1981
Tree automata generalize the notion of a finite automaton working on strings to that of a finite automaton operating on trees. Most results for finite automata have been extended to tree automata. In this paper we introduce tree derivatives which extend the concept of Brzozowski's string derivatives.
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