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Measure-Theoretic Probability With Applications to Statistics, Finance, and Engineering
This textbook offers an approachable introduction to measure-theoretic probability, illustrating core concepts with examples from statistics and...
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Measure Theory and Integration
This textbook contains a detailed and thorough exposition of topics in measure theory and integration. With abundant solved examples and more than...
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Measure
We recollect the essential concepts and results from Measure Theory, mostly without proofs. We state the Monotone class theorem, Carathéodory’s...
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Signed Measure
This chapter is on signed measures. The Jordan–Hahn theorem decomposes a signed measure into the difference of two measures in a unique way. This...
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Measure-Valued Branching Markov Processes
This book provides a compact introduction to the theory of measure-valued branching processes, immigration processes and Ornstein–Uhlenbeck type...
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Measure-Theoretic Calculus in Abstract Spaces On the Playground of Infinite-Dimensional Spaces
This monograph provides a rigorous, encyclopedic treatment of the fundamental topics in real analysis, functional analysis, and measure theory. The...
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Angle Measure
Like area measure, angle measure is a construct that can either be primitive or defined.
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Measure Theory
The concept of a measure is a generalization and formalization of length, area, volume, and other common notions such as mass and probability of...
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Area Measure
An area measure function A can be introduced either as another primitive construct or as a defined construct.
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Abstract Measure Theory
The objective of this chapter is to extend measure theory by generalizing the concept of measure to include more general sets other than sets in...
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Measure Theory
There is a motivation to generalize the notion of length to another concept that could capture length in a more general setting. In principle, the...
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Determination of the Extremal Measure
The chapter deals with the problem how to determine the (weighted) equilibrium measure and its support. Various classical procedures from Fourier...
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The Haar Measure
It is well known that every locally compact group admits a (one sided) translation invariant Haar measure. Applications of the Haar measure in...
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Measure-Valued Structured Deformations
Measure-valued structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a...
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Segmentation in Measure Spaces
We consider an abstract concept of perimeter measure space as a very general framework in which one can properly consider two of the most...
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Quaternionic Monge–Ampère Measure on Pluripolar Set
In this paper, we prove that in a hyperconvex domain Ω in ℍ n , if a non-negative Borel measure is dominated by a quaternionic Monge–Ampère measure,...
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General Measure and Integration
The first five sections of this chapter are dedicated to the study of measure theory, measurable functions on a measure space, general integration...
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Multiplicative arithmetic functions and the generalized Ewens measure
Random integers, sampled uniformly from [1, x ], share similarities with random permutations, sampled uniformly from S n . These similarities include...
