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On covering systems Mallory, Donald James
Abstract
This paper is concerned with the relationships between certain covering systems useful for set differentiation and with their application to density theorems and approximate continuity. The covering systems considered are the Vitali systems (which we call V-systems), the systems introduced by Sion (which we call S-systems), and a modification of the tile systems (which we call T-systems). It is easily checked from the definitions that V-systems are S-systems, and under slight restrictions, T-systems. We show also that under certain conditions S-systems are T-systems, and that in general the converses do not hold. Density theorems and the relationships between approximate continuity and measurability of functions are discussed for these systems. In particular, we prove that for T-systems measurable functions are approximately continuous and hence a density theorem holds.
Item Metadata
Title |
On covering systems
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1962
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Description |
This paper is concerned with the relationships between certain covering systems useful for set differentiation and with their application to density theorems and approximate continuity.
The covering systems considered are the Vitali systems (which we call V-systems), the systems introduced by Sion (which we call S-systems), and a modification of the tile systems (which we call T-systems).
It is easily checked from the definitions that V-systems are S-systems, and under slight restrictions, T-systems. We show also that under certain conditions S-systems are T-systems, and that in general the converses do not hold.
Density theorems and the relationships between approximate continuity and measurability of functions are discussed for these systems.
In particular, we prove that for T-systems measurable functions are approximately continuous and hence a density theorem holds.
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Genre | |
Type | |
Language |
eng
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Date Available |
2011-11-10
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080586
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.