Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Infimum and Supremum of the Set of Real Numbers.
Measure Theory

Jozef Bialas

University of Lodz
Summary.

We introduce some properties of the least upper bound and
the greatest lower bound of the subdomain of $\overline{\Bbb R}$ numbers, where $\overline{\Bbb R}$
denotes the enlarged set of real numbers, $\overline{\Bbb R} = {\Bbb R} \cup \{\infty,+\infty\}$.
The paper contains definitions of majorant and minorant elements, bounded
from above, bounded from below and bounded sets, sup and inf of set, for
nonempty subset of $\overline{\Bbb R}$. We prove theorems describing the basic
relationships among those definitions. The work is the first part
of the series of articles concerning the Lebesgue measure theory.
The terminology and notation used in this paper have been
introduced in the following articles
[3]
[2]
[5]
[1]
[4]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The ordinal numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [4]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [5]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
Received September 27, 1990
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