Approximation, complete continuity, and uniform measurability of Uryson operators on general measure spaces

1998 ◽  
Vol 33 (7) ◽  
pp. 715-728 ◽  
Author(s):  
M. Väth
Keyword(s):  
General Measure ◽  
Complete Continuity ◽  
Measure Spaces

On (L1)* for General Measure Spaces

1963 ◽  
Vol 6 (2) ◽  
pp. 211-229 ◽  
Author(s):  
H. W. Ellis ◽  
D. O. Snow
Keyword(s):  
Measurable Function ◽  
Measure Space ◽  
Finite Measure ◽  
Signed Measure ◽  
General Measure ◽  
Measure Spaces ◽  
Arbitrary Measure ◽  
Image Position ◽  
Nikodym Theorem

It is well known that certain results such as the Radon-Nikodym Theorem, which are valid in totally σ -finite measure spaces, do not extend to measure spaces in which μ is not totally σ -finite. (See §2 for notation.) Given an arbitrary measure space (X, S, μ) and a signed measure ν on (X, S), then if ν ≪ μ for X, ν ≪ μ when restricted to any e ∊ Sf and the classical finite Radon-Nikodym theorem produces a measurable function ge(x), vanishing outside e, with

Extensions of the Borel–Cantelli lemma in general measure spaces

2013 ◽  
Vol 27 (4) ◽  
pp. 1229-1248 ◽  
Author(s):  
Xuejun Wang ◽  
Xinghui Wang ◽  
Xiaoqin Li ◽  
Shuhe Hu
Keyword(s):  
Cantelli Lemma ◽  
General Measure ◽  
Measure Spaces

General Measure Spaces

Real Analysis ◽  
2016 ◽  
pp. 95-108
Author(s):  
Peter A. Loeb
Keyword(s):  
General Measure ◽  
Measure Spaces

STEFFENSEN TYPE INEQUALITIES OVER GENERAL MEASURE SPACES

Analysis ◽  
1997 ◽  
Vol 17 (2-3) ◽  
pp. 301-322 ◽  
Author(s):  
Jean-Claude Evard ◽  
Hillel Gauchman
Keyword(s):  
General Measure ◽  
Measure Spaces

On the Basis Problem for Vector Valued Function Spaces

1956 ◽  
Vol 8 ◽  
pp. 417-422 ◽  
Author(s):  
H. W. Ellis
Keyword(s):  
Banach Spaces ◽  
Function Spaces ◽  
Length Function ◽  
General Measure ◽  
Basis Problem ◽  
Measure Spaces ◽  
Vector Valued Function ◽  
Vector Valued

1. Introduction. In a recent paper (2) Halperin and the author considered separable Banach spaces Lλ of real valued functions on general measure spaces and proved the existence of 1-regular (§2) Haar or σ-Haar bases when λ was the classical p-norm or any levelling length function (3) and, more generally, of K-regular Haar or σ-Haar bases when λ was a continuous length function satisfying certain additional conditions (2, Theorem 3.2).

scholarly journals Rearrangement transformations on general measure spaces

2008 ◽  
Vol 19 (1) ◽  
pp. 33-51 ◽  
Author(s):  
Santiago Boza ◽  
Javier Soria
Keyword(s):  
General Measure ◽  
Measure Spaces
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