Name
Abstract | ||
|---|---|---|
The theory of integration over infinite-dimensional spaces is known to encounter serious difficulties. Categorical ideas seem to arise naturally on the path to a remedy. Such an approach was suggested and initiated by Segal in his pioneering article (Segal, Bull Am Math Soc 71:419–489, ). In our paper we follow his ideas from a different perspective, slightly more categorical, and strongly inspired by the point-free topology. First, we develop a general (point-free) concept of measurability (extending the standard Lebesgue integration when applying to the classical -algebra). Second (and here we have a major difference from the classical theory), we prove that every finite-additive function with values in [0,1] can be extended to a measure on an abstract -algebra; this correspondence is functorial and yields uniqueness. As an example we show that the Segal space can be characterized by completely canonical data. Furthermore, from our results it follows that a satisfactory point-free integration arises everywhere where we have a finite-additive probability function on a Boolean algebra. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/s10485-012-9295-2 | Applied Categorical Structures |
Keywords | DocType | Volume |
Point free measures,Boolean rings,Categorical geometry,Locales,Segal space,28A60,16B50,03G30,28C20 | Journal | 22 |
Issue | ISSN | Citations |
1 | 0927-2852 | 0 |
PageRank | References | Authors |
0.34 | 1 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Igor Kríz | 1 | 3 | 1.88 |
| Ales Pultr | 2 | 72 | 24.12 |