Topics in Measure Theory and Real Analysis

• Κύριος συγγραφέας: Kharazishvili, Alexander B. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Paris : Atlantis Press, 2009.
• Σειρά: Atlantis Studies in Mathematics, 2
• Θέματα: Mathematics.; Measure theory.; Measure and Integration.

This book highlights various topics on measure theory and vividly demonstrates that the different questions of this theory are closely connected with the central measure extension problem. Several important aspects of the measure extension problem are considered separately: set-theoretical, topologi...

Πίνακας περιεχομένων:

• 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 Sierpi?ski-Zygmund functions
• Relatively measurable Sierpi?ski-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.