1. SummaryWe develop a theory of probability on Boolean and Heyting algebras. By [8], complete probability Heyting algebras and their complete products exist. Therefore we can talk about sequences of independent random variables on a complete Heyting algebra. We are able to define integral, expectation and variance for such random variables. The results can be used in physics, for example in S. Bellert's cosmology, as shown in [7] and [9]. Implications of probability theory on Boolean algebras in mathematical foundations of quantum physics are far-reaching and well known.
CONTENTS1. Summary..............................................................................................................52. Spectral measure theory for Boolean and Heyting algebras................................52.1. Introduction.......................................................................................................52.2. Spectral measures for Boolean algebras..........................................................52.3. Spectral supermeasures for Heyting algebras.................................................113. Theory of the integral for Boolean and Heyting algebras...................................143.1. Introduction.....................................................................................................143.2. Theory of the integral......................................................................................144. Some numerical characteristics of random variables on Heyting algebras.........184.1. Introduction.....................................................................................................184.2. Expectation and variance................................................................................184.3. Other fundamental numerical characteristics of random variables..................24References............................................................................................................28
@book{bwmeta1.element.zamlynska-d1406e4a-f257-4385-9972-e8164240f99d,
author = {Ewa Rydzy\'nska},
title = {Random variables on Boolean and Heyting algebras and their numerical characteristics},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1990},
zbl = {0705.60002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-d1406e4a-f257-4385-9972-e8164240f99d}
}
Ewa Rydzyńska. Random variables on Boolean and Heyting algebras and their numerical characteristics. GDML_Books (1990), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-d1406e4a-f257-4385-9972-e8164240f99d/