Measure Theory
A measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, volume, etc. Measure theory is concerned with generalizing the notions of area on arbitrary sets of Euclidean spaces and notions of length of subsets of R. Essentially, it is a common ground for analysis of real functions and set theory.
A first course in measure theory will most likely devote time to many of the following topics:
 Functions and Integrals
 Convergence
 Signed and Complex Measures
 Product Measures
 Differentiation
 Measures on Locally Compact Spaces
 Polish Spaces and Analytic Sets
 Haar Measure
 Operations on Measures
 Extensions
 Structural Characteristics for Set Functions
 Measurable Functions on Monotone Measure Spaces
 Integration
 Sugeno Integrals
 PanIntegrals
 Choquet Integrals
 Upper and Lower Integrals
 Constructing General Measures
 Fuzzification of Generalized Measures and the Choquet Integral
 Applications of Generalized Measure Theory
A graduate level text on measure theory is available on Amazon.com. Students can find a large number of books on this topic on Google, and there are some measure theory tutorials available online.
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