On "Essentially Metrizable" Spaces and on Measurable Functions with Values in Such Spaces

Elias Zakon

doi:10.2307/1994078

On ‘‘essentially metrizable” spaces and on measurable functions with values in such spaces

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-1965-0218517-5 ◽

1965 ◽

Vol 119 (3) ◽

pp. 443-443

Author(s):

Elias Zakon

Keyword(s):

Measurable Functions ◽

Metrizable Spaces

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CLASSIFICATIONS OF BOREL MEASURABLE FUNCTIONS

Real Analysis Exchange ◽

10.2307/44152516 ◽

1994 ◽

Vol 20 (2) ◽

pp. 407

Author(s):

Morayne

Keyword(s):

Measurable Functions ◽

Borel Measurable

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Universal elements for families of separable metrizable spaces

Journal of Mathematical Sciences ◽

10.1007/bf02434916 ◽

1998 ◽

Vol 91 (6) ◽

pp. 3387-3415

Author(s):

D. N. Georgiou ◽

S. D. Iliadis

Keyword(s):

Metrizable Spaces

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Lacunary ideal convergence in measure for sequences of fuzzy valued functions

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202624 ◽

2021 ◽

Vol 40 (3) ◽

pp. 5517-5526

Author(s):

Ömer Kişi

Keyword(s):

Measure Space ◽

Finite Measure ◽

Ideal Convergence ◽

Convergence In Measure ◽

Ideal Form ◽

Measurable Functions ◽

Finite Measure Space ◽

Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

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Several results on compact metrizable spaces in $$\mathbf {ZF}$$

Monatshefte für Mathematik ◽

10.1007/s00605-021-01582-0 ◽

2021 ◽

Author(s):

Kyriakos Keremedis ◽

Eleftherios Tachtsis ◽

Eliza Wajch

Keyword(s):

Continuum Hypothesis ◽

Compact Spaces ◽

Power Set ◽

Compact Metrizable Space ◽

Permutation Models ◽

Independence Results ◽

The Axiom Of Choice ◽

Metrizable Spaces ◽

Transfer Theorems ◽

The Continuum

AbstractIn the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

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On a Singular Two-Point Boundary Value Problem for the Nonlinear mth-Order Differential Equation with Deviating Arguments

Georgian Mathematical Journal ◽

10.1515/gmj.1997.557 ◽

1997 ◽

Vol 4 (6) ◽

pp. 557-566

Author(s):

B. Půža

Keyword(s):

Differential Equation ◽

Boundary Value Problem ◽

Vector Function ◽

Unique Solvability ◽

Order Differential Equation ◽

Boundary Value ◽

Sufficient Conditions ◽

Point Boundary ◽

Deviating Arguments ◽

Measurable Functions

Abstract Sufficient conditions of solvability and unique solvability of the boundary value problem u (m)(t) = f(t, u(τ 11(t)), . . . , u(τ 1k (t)), . . . , u (m–1)(τ m1(t)), . . . . . . , u (m–1)(τ mk (t))), u(t) = 0, for t ∉ [a, b], u (i–1)(a) = 0 (i = 1, . . . , m – 1), u (m–1)(b) = 0, are established, where τ ij : [a, b] → R (i = 1, . . . , m; j = 1, . . . , k) are measurable functions and the vector function f : ]a, b[×Rkmn → Rn is measurable in the first and continuous in the last kmn arguments; moreover, this function may have nonintegrable singularities with respect to the first argument.

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