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Topological aspects of the space of metric measure spaces
Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces...
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Approximate Methods for Solving Chance-Constrained Linear Programs in Probability Measure Space
A risk-aware decision-making problem can be formulated as a chance-constrained linear program in probability measure space. Chance-constrained linear...
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Weighted Sobolev Type Inequalities in a Smooth Metric Measure Space
In this paper, we obtain weighted Sobolev type inequalities with explicit constants that extend the inequalities obtained by Guo et al. (Math Res...
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On a Reverse Integral Hardy Inequality on Polarisable Metric Measure Space
In this short note, we give reverse integral Hardy inequalities on polarisable metric measure space in the case...
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Median-Type John–Nirenberg Space in Metric Measure Spaces
We study the so-called John–Nirenberg space that is a generalization of functions of bounded mean oscillation in the setting of metric measure spaces...
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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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Convergence of Bergman measures towards the Zhang measure
We prove that the Bergman measure along a holomorphic family of curves parametrized by the punctured unit disk converges to the Zhang measure on the...
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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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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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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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Winding of geodesic rays chosen by a harmonic measure
We prove limit theorems for the homological winding of geodesic rays distributed via a harmonic measure on a Gromov hyperbolic space. We obtain...
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Existence of Integro-Differential Neutral Measure Driven System Using Monotone Iterative Technique and Measure of Noncompactness
In present manuscript, we bring into work the technique of lower and upper solutions incorporated with the monotone iterative technique to discuss...