zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Absolutely abnormal numbers. (English) Zbl 1036.11035
A real number x between 0 and 1 is called normal to the base b, an integer >1, if the digits in the b n -ary expansion of x are asymptotically uniformly distributed for every fixed positive integer n. If x is normal to every base b, then x is called absolutely normal. On the other hand, a number x is abnormal to the base b if x is not normal, and x is absolutely abnormal, if it is abnormal to every base. While it is easy to construct absolutely normal numbers, it is far more difficult to find numbers which are absolutely abnormal. A reason for the second claim is partially due to the fact that, with respect to Lebesgue measure, almost all numbers are absolutely normal. The author constructs absolutely abnormal numbers and then shows that the constructed number has the required property.

11K16Normal numbers, etc.
11A63Radix representation; digital problems