Mathematical Logic Quarterly 53 (4):415-430 (2007)

Abstract
By the Riesz representation theorem for the dual of C [0; 1], if F: C [0; 1] → ℝ is a continuous linear operator, then there is a function g: [0;1] → ℝ of bounded variation such that F = ∫ f dg . The function g can be normalized such that V = ‖F ‖. In this paper we prove a computable version of this theorem. We use the framework of TTE, the representation approach to computable analysis, which allows to define natural computability for a variety of operators. We show that there are a computable operator S mapping g and an upper bound of its variation to F and a computable operator S ′ mapping F and its norm to some appropriate g
Keywords Computable analysis  Riesz representation theorem  integration
Categories (categorize this paper)
DOI 10.1002/malq.200710008
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,008
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Computable Metrization.Tanja Grubba, Matthias Schröder & Klaus Weihrauch - 2007 - Mathematical Logic Quarterly 53 (4‐5):381-395.
Borel Complexity and Computability of the Hahn–Banach Theorem.Vasco Brattka - 2008 - Archive for Mathematical Logic 46 (7-8):547-564.
Finite Computable Dimension Does Not Relativize.Charles F. D. McCoy - 2002 - Archive for Mathematical Logic 41 (4):309-320.
Primitive Recursive Real Numbers.Qingliang Chen, Kaile Kaile & Xizhong Zheng - 2007 - Mathematical Logic Quarterly 53 (4):365-380.
A Uniformly Computable Implicit Function Theorem.Timothy H. McNicholl - 2008 - Mathematical Logic Quarterly 54 (3):272-279.
An Example Related to Gregory’s Theorem.J. Johnson, J. F. Knight, V. Ocasio & S. VanDenDriessche - 2013 - Archive for Mathematical Logic 52 (3-4):419-434.
Recursive Approximability of Real Numbers.Xizhong Zheng - 2002 - Mathematical Logic Quarterly 48 (S1):131-156.
Computational Complexity on Computable Metric Spaces.Klaus Weirauch - 2003 - Mathematical Logic Quarterly 49 (1):3-21.

Analytics

Added to PP index
2013-12-01

Total views
6 ( #1,132,778 of 2,505,153 )

Recent downloads (6 months)
1 ( #416,587 of 2,505,153 )

How can I increase my downloads?

Downloads

My notes