Several Properties of the $\sigma$-additive Measure

Jozef Bialas

University of Lodz

Summary.

A continuation of [4]. The paper contains the definition and basic properties of a $\sigma$-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 R.~Sikorski [9]. Some simple theorems concerning basic properties of a $\sigma$-additive measure, measurable sets, measure zero sets are proved. The work is the fourth part of the series of articles concerning the Lebesgue measure theory.

MML Identifier: MEASURE2

Contents (PDF format)

Bibliography

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