On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions (Q2848709)
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scientific article; zbMATH DE number 6212154
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions |
scientific article; zbMATH DE number 6212154 |
Statements
26 September 2013
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cádlág function
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total variation
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truncated variation
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uniform approximation
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regulated function
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0.8531866
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0.8479158
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0.8426799
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0.8425932
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0.8412849
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0.8409986
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0.8401574
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0.84006214
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On a generalisation of the Hahn-Jordan decomposition for real càdlàg functions (English)
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Cádlág functions (also known as RCLL functions -- right continuous with left limits) are studied with respect to their total variation on a compact real interval. The first problem is estimating the greatest lower bound for a function \(g\) uniformly approximating a given cádlág function \(f\) with prescribed accuracy. The second problem is finding the greatest lower bound of the total variation for \(f+h\), where \(h\) is an arbitrary function with bounded oscillation.
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