Note on a Theorem of Myrberg

Author:

Gillis J.

Abstract

1. Prof. Fekete, in a letter to the author, wrote: “…Satz von Myrberg über den Zusammenhang zwischen dem transfiniten Durchmesser und dem logarithmischen Mass zugehörig zum Exponenten 1 + ε, ε > 0 (vgl. Satz 10 in seiner Acta Arbeit).…Ich würde einen elementaren Beweis für den letzteren Satz sehr begrüssen.” The object of this note is to supply such a proof but, since the concepts involved may not all be matters of common knowledge, I shall begin by outlining the necessary definitions, the relevant known results, the nature of the theorem and its relation to what is known.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference10 articles.

1. �ber den transfiniten Durchmesser ebener Punktmengen

2. Erdös P. and Gillis J. , “Note on the transfinite diameter”, Journ. Lond. Math. Soc. (in the press).

3. Dimension und �u�eres Ma�

4. On linear sets of points of fractional dimension

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