Jordan Measure and Riemann Integration

@article{Frink1933JordanMA,
  title={Jordan Measure and Riemann Integration},
  author={Orrin Frink},
  journal={Annals of Mathematics},
  year={1933},
  volume={34},
  pages={518}
}
  • O. Frink
  • Published 1 July 1933
  • Mathematics
  • Annals of Mathematics
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math.uga.edu
18 Citations
Background Citations
5
Methods Citations
2

18 Citations

A Finite Graph Approach to the Probabilistic Hadwiger-Nelson Problem.

The numerical numerical badness of a given $k$-coloring of the plane is defined to be the probability that a randomly chosen unit-distance edge is monochromatic under the coloring, and lower bounds on the badness are provided using a probabilistic technique relating to finite graphs.

Finitely Additive Measures on Topological Spaces and Boolean Algebras, University of East Anglia, UK, 2015. Supervised by Mirna Džamonja

Zanyar Anwer Ameen, Finitely Additive Measures on Topological Spaces and Boolean Algebras, University of East Anglia, UK, 2015.

Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients

In this work, we present a generalized methodology for analyzing the convergence of quasi-optimal Taylor and Legendre approximations, applicable to a wide class of parameterized elliptic PDEs with…

Analysis of quasi-optimal polynomial approximations for parameterized PDEs with deterministic and stochastic coefficients

In this work, we present a generalized methodology for analyzing the convergence of quasi-optimal Taylor and Legendre approximations, applicable to a wide class of parameterized elliptic PDEs with…

An axiomatic integral and a multivariate mean value theorem

In order to investigate minimal sufficient conditions for an abstract integral to belong to the convex hull of the integrand, we propose a system of axioms under which it happens. If the integrand is…

Semiclassical measures for the Schrödinger equation on the torus

In this article, the structure of semiclassical measures for solutions to the linear Schrödinger equation on the torus is analysed. We show that the disintegration of such a measure on every…

ON SOME MEASURE THEORY TEXTBOOKS AND THEIR USE BY SOME PROFESSORS IN GRADUATE-LEVEL COURSES

This thesis investigates one instructor's account of his use of a textbook and two mathematics professors' views of which textbook they would use and how if they were to teach a Measure Theory course at the graduate level.

Geometry of Numbers with Applications to Number Theory

1. Lattices in Euclidean Space 3 1.1. Discrete vector groups 3 1.2. Hermite and Smith Normal Forms 5 1.3. Fundamental regions, covolumes and sublattices 6 1.4. The Classification of Vector Groups 12…

Strongly Consistent Estimation of the Sample Distribution of Noisy Continuous-Parameter Fields

By “uniformly sampling” such random fields the difficulties may be avoided and a sample distribution may be compatibly defined and determined, and the obtained result resembles the known fact that the probability distribution of the sum of two independent random variables is the convolution of their distributions.

Abstract Riemann integrability and measurability

We prove that the spectral sets of any positive abstract Riemann integrable function are measurable but (at most) a countable amount of them. In addition, the integral of such a function can be…