Construction of \mu-normal sequences
Manfred G. Madritsch, Bill Mance
TL;DR
This paper extends the construction of normal sequences to generate -normal sequences for various expansions, providing a method to produce sequences generic for any invariant measure, not just the maximal one.
Contribution
It introduces a new construction method for -normal sequences that are generic for arbitrary invariant measures, expanding beyond traditional maximal measure cases.
Findings
Constructed -normal sequences for L roth, continued fractions, and -expansions.
Provided estimates and examples demonstrating the construction.
Extended the concept of normal numbers to sequences generic for non-maximal measures.
Abstract
In the present paper we extend Champernowne's construction of normal numbers to provide sequences which are generic for a given invariant probability measure, which need not be the maximal one. We present a construction together with estimates and examples for normal numbers with respect to L\"uroth series expansion, continued fractions expansion or -expansion.
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