Burkholder theorem in Riesz spaces

Rough weighted statistical convergence on locally solid Riesz spaces

Positivity ◽

10.1007/s11117-021-00843-4 ◽

2021 ◽

Author(s):

Sanjoy Ghosal ◽

Mandobi Banerjee

Keyword(s):

Statistical Convergence ◽

Riesz Spaces

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Correction to: Disjointness preserving operators on normed pre-Riesz spaces: extensions and inverses

Positivity ◽

10.1007/s11117-020-00743-z ◽

2020 ◽

Vol 24 (2) ◽

pp. 505-505

Author(s):

Anke Kalauch ◽

Onno van Gaans ◽

Feng Zhang

Keyword(s):

Riesz Spaces ◽

Disjointness Preserving

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Small Riesz spaces

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100077902 ◽

1989 ◽

Vol 105 (3) ◽

pp. 523-536 ◽

Cited By ~ 20

Author(s):

G. Buskes ◽

A. van Rooij

Keyword(s):

Representation Theory ◽

Direct Method ◽

Riesz Space ◽

Pictorial Representation ◽

Representation Theorems ◽

Riesz Spaces ◽

Number Of Authors

Many facts in the theory of general Riesz spaces are easily verified by thinking in terms of spaces of functions. A proof via this insight is said to use representation theory. In recent years a growing number of authors has successfully been trying to bypass representation theorems, judging them to be extraneous. (See, for instance, [9,10].) In spite of the positive aspects of these efforts the following can be said. Firstly, avoiding representation theory does not always make the facts transparent. Reading the more cumbersome constructions and procedures inside the Riesz space itself one feels the need for a pictorial representation with functions, and one suspects the author himself of secret heretical thoughts. Secondly, the direct method leads to repeating constructions of the same nature over and over again.

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A Fubini Theorem in Riesz spaces for the Kurzweil-Henstock Integral

Journal of Function Spaces and Applications ◽

10.1155/2011/158412 ◽

2011 ◽

Vol 9 (3) ◽

pp. 283-304 ◽

Cited By ~ 4

Author(s):

A. Boccuto ◽

D. Candeloro ◽

A. R. Sambucini

Keyword(s):

Type Theorem ◽

Riesz Space ◽

Fubini Theorem ◽

Real Plane ◽

Henstock Integral ◽

Riesz Spaces

A Fubini-type theorem is proved, for the Kurzweil-Henstock integral of Riesz-space-valued functions defined on (not necessarily bounded) subrectangles of the “extended” real plane.

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