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1. The Measurability of RealValued Functions
"... Summary. Based on [16], authors formalized the integral of an extended real valued measurable function in [12] before. However, the integral argued in [12] cannot be applied to realvalued functions unconditionally. Therefore, in this article we have formalized the integral of a realvalue function. ..."
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Summary. Based on [16], authors formalized the integral of an extended real valued measurable function in [12] before. However, the integral argued in [12] cannot be applied to realvalued functions unconditionally. Therefore, in this article we have formalized the integral of a realvalue function.
On the Decomposition of RealValued Functions
, 1994
"... The decomposition of discrete (especially binary) functions has long been useful for developing theoretical properties of function representations and more recently as a design method for FPGAs. Because of its fundamental character, function decomposition is also of interest as an approach to comput ..."
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Cited by 10 (5 self)
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to computational learning and pattern finding in general. Within this "pattern finding" application of function decomposition, there are problems that are best modeled as a function whose inputs and outputs are from a continuum (especially the real numbers). We examine the decomposition process
RealValued Functions On Flows
, 1996
"... We develop the flow analog of the classical Yosida adjunction between spaces and archimedean latticeordered groups with strong unit. A product of this development is the flow counterpart of the classical compactification of a space. We characterize those flows which are compactifiable, i.e., dense ..."
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Cited by 3 (0 self)
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We develop the flow analog of the classical Yosida adjunction between spaces and archimedean latticeordered groups with strong unit. A product of this development is the flow counterpart of the classical compactification of a space. We characterize those flows which are compactifiable, i.e., dense subflows of a compact flow. Finally, we exhibit a duality between the compactifications of a given flow and the topologies on the monoid of actions.
Maxitive Integral of RealValued Functions
"... www.statistik.lmu.de/~cattaneo Abstract. The paper pursues the definition of a maxitive integral on all realvalued functions (i.e., the integral of the pointwise maximum of two functions must be the maximum of their integrals). This definition is not determined by maxitivity alone: additional requi ..."
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www.statistik.lmu.de/~cattaneo Abstract. The paper pursues the definition of a maxitive integral on all realvalued functions (i.e., the integral of the pointwise maximum of two functions must be the maximum of their integrals). This definition is not determined by maxitivity alone: additional
Inferability of Recursive RealValued Functions
 Moscow Math. Soc
, 1997
"... This paper presents a method of inductive inference of realvalued functions from given pairs of observed data of (x; h(x)), where h is a target function to be inferred. Each of such observed data inevitably involves some ranges of errors, and hence it is usually represented by a pair of rational nu ..."
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Cited by 1 (1 self)
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This paper presents a method of inductive inference of realvalued functions from given pairs of observed data of (x; h(x)), where h is a target function to be inferred. Each of such observed data inevitably involves some ranges of errors, and hence it is usually represented by a pair of rational
Efficiently Approximable RealValued Functions
 Electronic Colloquium on Computational Complexity
, 2000
"... We consider a class, denoted APP, of realvalued functions f : f0; 1g n ! [0; 1] such that f can be approximated, to within any ffl ? 0, by a probabilistic Turing machine running in time poly(n; 1=ffl). We argue that APP can be viewed as a generalization of BPP, and show that APP contains a nat ..."
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Cited by 13 (2 self)
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We consider a class, denoted APP, of realvalued functions f : f0; 1g n ! [0; 1] such that f can be approximated, to within any ffl ? 0, by a probabilistic Turing machine running in time poly(n; 1=ffl). We argue that APP can be viewed as a generalization of BPP, and show that APP contains a
Statistical Convergence of Double Sequences of RealValued Functions
"... In this study, we introduce the notion of pointwise and uniform statistical convergence of double sequences of realvalued functions. We also give the relations between these convergences and pointwise,uniform convergence. Furthermore, we introduce the concept of statistically Cauchy sequence and st ..."
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In this study, we introduce the notion of pointwise and uniform statistical convergence of double sequences of realvalued functions. We also give the relations between these convergences and pointwise,uniform convergence. Furthermore, we introduce the concept of statistically Cauchy sequence
Fatshattering and the learnability of realvalued functions
 Journal of Computer and System Sciences
, 1996
"... We consider the problem of learning realvalued functions from random examples when the function values are corrupted with noise. With mild conditions on independent observation noise, we provide characterizations of the learnability of a realvalued function class in terms of a generalization of th ..."
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Cited by 82 (10 self)
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We consider the problem of learning realvalued functions from random examples when the function values are corrupted with noise. With mild conditions on independent observation noise, we provide characterizations of the learnability of a realvalued function class in terms of a generalization
1. Partial Sums of RealValued Functional Sequences
"... Summary. In this article, we formalized Lebesgue’s Convergence theorem of complexvalued function. We proved Lebesgue’s Convergence Theorem of realvalued function using the theorem of extensional realvalued function. Then applying the former theorem to real part and imaginary part of complexvalued ..."
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Summary. In this article, we formalized Lebesgue’s Convergence theorem of complexvalued function. We proved Lebesgue’s Convergence Theorem of realvalued function using the theorem of extensional realvalued function. Then applying the former theorem to real part and imaginary part of complexvalued
A continuous derivative for realvalued functions
 New Computational Paradigms, Changing Conceptions of What is Computable
, 2008
"... We develop a notion of derivative of a realvalued function on a Banach space, called the Lderivative, which is constructed by introducing a generalization of Lipschitz constant of a map. As with the Clarke gradient, the values of the Lderivative of a function are nonempty weak * compact and conv ..."
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Cited by 4 (4 self)
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We develop a notion of derivative of a realvalued function on a Banach space, called the Lderivative, which is constructed by introducing a generalization of Lipschitz constant of a map. As with the Clarke gradient, the values of the Lderivative of a function are nonempty weak * compact
Results 1  10
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