Journal of Formalized Mathematics
Volume 2, 1990
University of Bialystok
Copyright (c) 1990
Association of Mizar Users
Series of Positive Real Numbers.
Measure Theory

Jozef Bialas

University of Lodz
Summary.

We introduce properties of a series of nonnegative
$\overline{\Bbb R}$ numbers, where $\overline{\Bbb R}$ denotes
the enlarged set of real numbers,
$\overline{\Bbb R} = {\Bbb R} \cup \{\infty,+\infty\}$.
The paper contains definition of sup $F$ and inf $F$, for $F$ being
function, and a definition of a sumable subset of $\overline{\Bbb R}$. We proved the basic
theorems regarding the definitions mentioned above.
The work is the second part of a series of articles concerning
the Lebesgue measure theory.
The terminology and notation used in this paper have been
introduced in the following articles
[7]
[9]
[8]
[6]
[3]
[10]
[4]
[5]
[1]
[2]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Grzegorz Bancerek.
Countable sets and Hessenberg's theorem.
Journal of Formalized Mathematics,
2, 1990.
 [3]
Jozef Bialas.
Infimum and supremum of the set of real numbers. Measure theory.
Journal of Formalized Mathematics,
2, 1990.
 [4]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [5]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [8]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [9]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received September 27, 1990
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