scientific article
From MaRDI portal
Publication:3708229
zbMath0583.26006MaRDI QIDQ3708229
Publication date: 1985
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Egoroff's theoreminfinitesimalsnon-standard analysisFubini's theoremintroductory textbookinfinitely large numbersnon-standard Banach space theorynon-standard treatment of the Riesz representation theoremultrapowers of the real number system
Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions (26-01) Nonstandard models in mathematics (03H05) Nonstandard functional analysis (46S20) Nonstandard analysis (26E35)
Related Items
A Daniell integral approach to nonstandard Kurzweil-Henstock integral ⋮ Nonstandard analysis and Dempster-Shafer theory ⋮ Mixing and double recurrence in probability groups ⋮ Comparing the structures of mathematical objects ⋮ Analytic Mappings on Hyperfinite Sets ⋮ Direct hyperfinite representations of finitely additive probabilities ⋮ Unnamed Item ⋮ Integration of Correspondences on Loeb Spaces ⋮ Hyperfinite transversal theory. II ⋮ Π₁¹ sets of unbounded Loeb measure ⋮ AN INFINITESIMAL ANALYSIS OF THE STOP-LOSS-START-GAIN STRATEGY ⋮ Hyperfinite Law of Large Numbers ⋮ MINIMAL AXIOMATIC FRAMEWORKS FOR DEFINABLE HYPERREALS WITH TRANSFER ⋮ Coarse-grained spin density-functional theory: Infinite-volume limit via the hyperfinite ⋮ ATTRACTORS AND NEO-ATTRACTORS FOR 3D STOCHASTIC NAVIER–STOKES EQUATIONS ⋮ On the prime spectrum of the ring of bounded nonstandard complex numbers ⋮ Stochastic Navier-Stokes equations ⋮ Equilibrium Pricing of Derivative Securities in Dynamically Incomplete Markets ⋮ COMPUTABILITY THEORY, NONSTANDARD ANALYSIS, AND THEIR CONNECTIONS ⋮ Lower and upper Loeb-integrals ⋮ Nonstandard analysis and jump conditions for converging shock waves ⋮ Formalizing Scientifically Applicable Mathematics in a Definitional Framework ⋮ Topological Aspects of Hybrid Processes ⋮ A new variational principle ⋮ Elementary stochastic calculus for finance with infinitesimals ⋮ Nonstandard Fock spaces ⋮ Forcing in nonstandard analysis ⋮ Pointwise analysis of scalar fields: A nonstandard approach ⋮ Characterization of colombeau generalized functions by their pointvalues ⋮ Robinson lattices and their spectra ⋮ Nonstandard hulls of ordered vector spaces ⋮ A nonstandard solution of the Korteweg-de Vries equation ⋮ Social choice correspondences with infinitely many agents: serial dictatorship ⋮ Reverse mathematics and parameter-free transfer ⋮ Nonstandard methods of completing quasi-uniform spaces ⋮ A constructive approach to nonstandard analysis ⋮ The structure of graphs all of whose Y-sections are internal sets ⋮ Mountain pass theorems without Palais-Smale conditions ⋮ A strong form of almost differentiability ⋮ A finite intersection property and the Loeb measurability of ultrafilters on hyperfinite sets ⋮ Internal approach to external sets and universes. I: Bounded set theory ⋮ Nonstandard integration theory in topological vector lattices ⋮ Nonstandard analysis of ordered sets ⋮ Countably determined sets and a conjecture of C. W. Henson ⋮ Internal approach to external sets and universes. II: External universes over the universe of bounded set theory ⋮ Dispensing with the continuum ⋮ Real functions as traces of infinite polynomials ⋮ Nonstandard methods in combinatorics and theoretical computer science ⋮ An Optimization of the Besicovitch Covering ⋮ Nonstandard analysis and constructivism? ⋮ A logic for arguing about probabilities in measure teams ⋮ Internal approach to external sets and universes. III. Partially saturated universes ⋮ Enlargements of functional algebras for the lambda calculus ⋮ New non-standard topologies ⋮ On the StrongL1Trend to Equilibrium for the Boltzmann Equation ⋮ Flat sets ⋮ Metric completions, the Heine-Borel property, and approachability ⋮ To be or not to be constructive, that is not the question ⋮ MARGIN TRADING THROUGH HYPER TIMELINE ⋮ A nonstandard approach to asymptotic fixed point theorems ⋮ Exact arbitrage, well-diversified portfolios and asset pricing in large markets. ⋮ Dynamic directed random matching ⋮ On Vervaat's sup vague topology ⋮ Examples of new nonstandard hulls of topological vector spaces ⋮ On the independence of correspondences ⋮ Nonstandard analysis in topology: nonstandard and standard compactifications ⋮ Functions of limited accumulation ⋮ A nonstandard Lévy-Khintchine formula and Lévy processes ⋮ Classical mechanics as quantum mechanics with infinitesimal \(\hslash\) ⋮ Nonstandard methods in measure theory ⋮ Louveau's theorem for the descriptive set theory of internal sets ⋮ A nonstandard characterization of realcompactness ⋮ Nonstandard hulls of lattice-normed ordered vector spaces ⋮ Every Borel function is monotone Borel ⋮ BOUNDED POLYNOMIALS AND HOLOMORPHIC MAPPINGS BETWEEN CONVEX SUBRINGS OF * ⋮ A nonstandard proof of the Riesz representation theorem for weakly compact operators on C(Ω) ⋮ On the theory of vector valued Loeb measures and integration ⋮ From Discrete to Continuous Financial Models: New Convergence Results For Option Pricing ⋮ Strong non-standard completeness for fuzzy logics ⋮ Strong counterexamples to Borel hyperdeterminacy ⋮ ERNA and Friedman's Reverse Mathematics ⋮ Programming with Infinitesimals: A While-Language for Hybrid System Modeling ⋮ A reduction technique for limit theorems in analysis and probability theory ⋮ A Note on Liftings of Linear Continuous Functionals ⋮ Pseudo-uniform convergence, a nonstandard treatment ⋮ Graphs with \(\boldsymbol\Pi^ 0_ 1(\kappa)\) \(Y\)-sections ⋮ Anastácio da Cunha and the concept of convergent series ⋮ Function spaces, cartesian closedness and nonstandard methods ⋮ Planning for the long run: programming with patient, Pareto responsive preferences ⋮ \(p\)-adic physics, non-well-founded reality and unconventional computing ⋮ Standard and nonstandard polynomial approximation ⋮ Nonstandard and standard compactifications of ordered topological spaces ⋮ Incommensurables and incomparables: On the conceptual status and the philosophical use of hyperreal numbers ⋮ Location choice in two-sided markets with indivisible agents ⋮ Seminormed \(\ast\)-subalgebras of \(\ell^{\infty}(X)\) ⋮ Nash equilibrium and generalized integration for infinite normal form games ⋮ Global existence and validity for the BBGKY hierarchy ⋮ Super-Brownian motion: Path properties and hitting probabilities ⋮ Lifting Theorems in Nonstandard Measure Theory ⋮ On the Extensions of Vector-Valued Loeb Measures ⋮ Nonstandard Topology on Function Spaces with Applications to Hyperspaces ⋮ Transfer theorems for \(\pi\)-monads ⋮ Reverse formalism 16 ⋮ An infinitesimal proof of the implicit function theorem ⋮ Connectedness and compactness on standard sets ⋮ Phase operator problem and macroscopic extension of quantum mechanics ⋮ The strength of compactness in computability theory and nonstandard analysis ⋮ Hyperalgebraic primitive elements for relational algebraic and topological algebraic models ⋮ Stochastic Euler equations on the torus ⋮ The three arrows of Zeno. Cantorian and non-Cantorian concepts of the continuum and of motion ⋮ On the relation between elementary partial difference equations and partial differential equations ⋮ The field of rational numbers is algebraically closed in some of its topological completions ⋮ Topological completions of the field of rational numbers which consist of Liouville numbers and rational numbers ⋮ Non-cooperative games on hyperfinite Loeb spaces ⋮ A theory of hyperfinite processes: The complete removal of individual uncertainty via exact LLN ⋮ The optimal differentiation basis and liftings of 𝐿^{∞} ⋮ Mechanizing Nonstandard Real Analysis ⋮ Optimal Stopping of Two-Parameter Processes on Nonstandard Probability Spaces ⋮ On a problem of common approximate fixed points ⋮ Numerosities of labelled sets: A new way of counting ⋮ Monads and realcompactness ⋮ Optimal control problems with unbounded constraint sets ⋮ Asymmetric completions of partial metric spaces ⋮ A nonstandard approach to the uniqueness problem for the Navier-Stokes equations ⋮ Hyperfinite quantum random walks.