CLASSIFICATIONS OF BOREL MEASURABLE FUNCTIONS

1994 ◽  
Vol 20 (2) ◽  
pp. 407
Author(s):  
Morayne
Keyword(s):  
Measurable Functions ◽  
Borel Measurable

scholarly journals Pointwise measurable functions

2004 ◽  
Vol 95 (2) ◽  
pp. 305
Author(s):  
Herman Render ◽  
Lothar Rogge
Keyword(s):  
Large Class ◽  
Metric Space ◽  
Measurable Function ◽  
Polish Space ◽  
Topological Spaces ◽  
Range Space ◽  
Compact Metric Space ◽  
Delta Set ◽  
Measurable Functions ◽  
Borel Measurable

We introduce the new concept of pointwise measurability. It is shown in this paper that a measurable function is measurable at each point and that for a large class of topological spaces the converse also holds. Moreover it can be seen that a function which is continuous at a point is Borel-measurable at this point too. Furthermore the set of measurability points is considered. If the range space is a $\sigma$-compact metric space, then this set is a $G_{\delta}$-set; if the range space is only a Polish space this is in general not true any longer.

scholarly journals On the difference property of Borel measurable functions

2010 ◽  
Vol 208 (1) ◽  
pp. 57-73
Author(s):  
Hiroshi Fujita ◽  
Tamás Mátrai
Keyword(s):  
Difference Property ◽  
Measurable Functions ◽  
The Difference ◽  
Borel Measurable

scholarly journals On the Dirichlet Problem in the Axiomatic Theory of Harmonic Functions

1963 ◽  
Vol 23 ◽  
pp. 73-96 ◽  
Author(s):  
N. Boboc ◽  
C. Constantinescu ◽  
A. Cornea
Keyword(s):  
Dirichlet Problem ◽  
Harmonic Functions ◽  
Riemann Surfaces ◽  
Minimum Principle ◽  
Continuous Functions ◽  
Axiomatic Theory ◽  
Measurable Functions ◽  
Bounded Functions ◽  
Compact Riemann Surfaces ◽  
Borel Measurable

In the frame of the recent axiomatic theories of harmonic functions [2], [3], [1], it has been shown that the continuous bounded functions on the boundaries of relatively compact open sets are resolutive [5], [1]. The aim of the present paper is to substitute in these results the continuous functions by Borel-measurable functions and to leave out the restriction that the open sets are relatively compact. H. Bauer has replaced the axiom 3 of Brelot’s axiomatic by two weaker axioms: the axiom of separation (Trennungsaxiom) and the axiom K1. Since the axiom of separation is not fulfilled in some important cases (e.g. the compact Riemann surfaces) we shall weaken this axiom too, substituting it by one of its consequences: the minimum principle for hyperharmonic functions.

scholarly journals Infinite products of Borel measurable functions

2008 ◽  
Vol 155 (17-18) ◽  
pp. 1996-2000 ◽  
Author(s):  
Katarzyna Chmielewska ◽  
Aleksander Maliszewski
Keyword(s):  
Infinite Products ◽  
Measurable Functions ◽  
Borel Measurable

scholarly journals On a Lindenbaum Composition Theorem

2019 ◽  
Vol 74 (1) ◽  
pp. 145-158
Author(s):  
Jaroslav Šupina ◽  
Dávid Uhrik
Keyword(s):  
Topological Space ◽  
Real Line ◽  
Topological Spaces ◽  
The Real ◽  
Measurable Functions ◽  
Borel Measurable ◽  
Composition Theorem ◽  
Perfectly Normal

Abstract We discuss several questions about Borel measurable functions on a topological space. We show that two Lindenbaum composition theorems [Lindenbaum, A. Sur les superpositions des fonctions représentables analytiquement, Fund. Math. 23 (1934), 15–37] proved for the real line hold in perfectly normal topological space as well. As an application, we extend a characterization of a certain class of topological spaces with hereditary Jayne-Rogers property for perfectly normal topological space. Finally, we pose an interesting question about lower and upper Δ02-measurable functions.

scholarly journals Algebras of Borel measurable functions

1992 ◽  
Vol 141 (3) ◽  
pp. 229-242
Author(s):  
Michał Morayne
Keyword(s):  
Measurable Functions ◽  
Borel Measurable
Sign in / Sign up

Export Citation Format

Share Document