The $\sigma$-additive Measure Theory

Jozef Bialas

University of Lodz

Summary.

The article contains definition and basic properties of $\sigma$-additive, nonnegative measure, with values in $\overline{\Bbb R}$, the enlarged set of real numbers, where $\overline{\Bbb R}$ denotes set $\overline{\Bbb R} = {\Bbb R} \cup \{-\infty,+\infty\}$ - by [9]. We present definitions of $\sigma$-field of sets, $\sigma$-additive measure, measurable sets, measure zero sets and the basic theorems describing relationships between the notion mentioned above. The work is the third part of the series of articles concerning the Lebesgue measure theory.

MML Identifier: MEASURE1

Contents (PDF format)

Bibliography

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