Table of Contents

The Problem of Extending Partial Functions; Some Aspects of the Measure Extension Problem; Invariant Measures; Quasi-Invariant Measures; Measurability Properties of Real-Valued Functions; Some Properties of Step-Functions Connected with Extensions of Measures; Almost Measurable Real-Valued Functions; Several Facts From General Topology; Weakly Metrically Transitive Measures and Nonmeasurable Sets; Nonmeasurable Subgroups of Uncountable Solvable Groups; Algebraic Sums of Measure Zero Sets; The Absolute Nonmeasurability of Minkowski's Sum of Certain Universal Measure Zero Sets; Absolutely Nonmeasurable Additive Sierpiński-Zygmund Functions; Relatively Measurable Sierpiński-Zygmund Functions; A Nonseparable Extension of the Lebesgue Measure Without New Null-Sets; Metrical Transitivity and Nonseparable Extensions of Invariant Measures; Nonseparable Left Invariant Measures on Uncountable Solvable Groups; Universally Measurable Additive Functionals; Some Subsets of the Euclidean Plane; Restrictions of Real-Valued Functions; Appendices: Some Set-Theoretical Facts and Constructions; The Choquet Theorem and Measurable Selectors; Borel Measures on Metric Spaces; Continuous Nowhere Approximately Differentiable Functions; Some Facts From the Commutative Groups; Elements of Descriptive Set Theory.