Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 17 of 17 for “"Lebesgue measure"”.
-
Lebesgue ▼-Measure and Riemann ▼-Integration
… involving the ▲ case (i.e., ▲-derivatives, ▲-measure, ▲-integrability, etc.) with only a brief mention of the ▼case. This thesis is designed to give a greater understanding of ▼-measurability and Riemann ▼-integration, as well as to give a comparison between ▲ and ▼-measurability. Furthermore, …
-
Hyperspace Topologies
… of closed subsets of R-n having n-dimensional Lebesgue measure zero. We conclude with the intersection of these two sets being a residual set representing the collection of uncountable, closed subsets of R-n having n-dimensional Lebesgue measure zero.
-
Strange Attractors of Uniform Flows (Cantor Set, Solenoid)
… of these attractors has positive 3-dimensional Lebesgue measure).
-
The Mattila-Sjölin Problem for Triangles
… distance problem which establishes a positive Lebesgue measure for the distance set instead of it having nonempty interior
-
An Introduction to the Lebesgue Integral
… of integrals, the most important of which is the Lebesgue integral. The Lebesgue integral allows one to integrate unbounded or discontinuous functions whose Riemann integral does not exist, and it has mathematical properties that the Riemann integral does not. The definition of the Lebesgue …
-
Optimal Simultaneous Confidence Bounds in Regression
… of having smaller average width with respect to Lebesgue measure over the region, when coverage probabilities are equated. These conditions are shown to hold for many important regression designs. A new class of bounds for which the coverage probability may be easily computed is introduced. Using …
-
On Beurling's Theory of Generalized Numbers
… offered. Finally we estimate the integral of a measure obtained by interpolating the integer counting measure and (essentially) the Lebesgue measure.
-
Higher-Dimensional Analogues of Two Theorems of Orponen on Exceptional Sets
… \cap A \big) = s-m$ has positive Lebesgue measure for almost every $V \in \mathbf{Gr}(n,m)$ provided $s > m$. Informally, for all but a few subspaces $V$, the shadow of $A$ on $V$ has the largest possible dimension, and there are many sections of $A$ orthogonal to $V$ of …
-
Stationary Density Computation of the Frobenius-Perron Operators Based on the Dirac Delta Function
… and computation of absolutely invariant measures have played an important role in this field. In this study, we focus on the computation of a nontrivial fixed point of Frobenius-Perron operators (F-P operators).</p> <p>Let <em>S</em>: [0,1] → [0,1] be a piecewise monotonic mapping, and …
-
Wigner functions for a class of semidirect product groups
… in G , with complement of (left or right) Haar measure zero; (ii) the group admits a square-integrable representation; (iii) the Lebesgue measure d X * in the dual of the Lie algebra can be decomposed as [Special characters omitted.] , [Special characters omitted.] where [Special characters …
-
Functions of subnormal operators
… i ≠ j. Let μ be a positive regular Borel measure supported on ∂D and let m denote normalized Lebesgue measure on ∂D. If L is a compact set such that ∂L ⊂ K and R(L) is a Dirichlet algebra and if ν = μof⁻¹, then the Lebesgue decomposition of ν|<sub>∂V</sub> with respect to harmonic measure …
-
Maximum principle, mean value operators and quasi boundedness in non-euclidean settings
… distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling …
-
Continuum Methods and Tightness Results for Non-Simple SLE and CLE: Existence, Interactions, and Metric Approximations
… whole-plane space-filling SLEκ parameterized by Lebesgue measure, and establish uniform estimates on its behavior as κ↑8. A tightness argument allows us to take a limit in law, yielding a continuous version of SLE8. The second part of the thesis addresses the construction of multiple SLEκ …
-
On the Fourier decay and the dimension of self-similar measures
… decay of the Fourier transform of self-similar measures on $\R$. An iterated function system (IFS) on $\R$ is a collection of maps $f_1, \dots, f_r$ with $f_i(x)=\lambda_i x+\tau_i$, where $|\lambda_i|<1$ and $\lambda_i, \tau_i \in \R$. The self-similar measure $\mu$ associated to an IFS and to …
-
Combinatorics and Metric Geometry
… + |B|$^{1/k}$, where |$\cdot$| is the Lebesgue measure and A + B := {a + b : a $\in$ A, b $\in$ B} is the Minkowski sum. Moreover, we have equality if and only if A,B are homothetic convex sets. The stability question, studied in many papers, asks how the distance to equality in BM …
-
Combinatorial Problems with Geometric Flavour
… and $\mathbb{R}^k$, endowed with the measure $|\cdot|$ representing cardinality and outer Lebesgue measure, respectively. One of the central questions in additive combinatorics is the inverse sumset problem of characterizing the finite subsets $A$ with small $\textit{doubling …