Random variables on Boolean and Heyting algebras and their numerical characteristics

Ewa Rydzyńska. Random variables on Boolean and Heyting algebras and their numerical characteristics. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1990. <http://eudml.org/doc/268640>.

@book{EwaRydzyńska1990,
abstract = {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},
author = {Ewa Rydzyńska},
keywords = {spectral measures for Boolean algebras; probability on Boolean and Heyting algebras; mathematical foundations of quantum physics},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Random variables on Boolean and Heyting algebras and their numerical characteristics},
url = {http://eudml.org/doc/268640},
year = {1990},
}

TY - BOOK
AU - Ewa Rydzyńska
TI - Random variables on Boolean and Heyting algebras and their numerical characteristics
PY - 1990
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - 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
LA - eng
KW - spectral measures for Boolean algebras; probability on Boolean and Heyting algebras; mathematical foundations of quantum physics
UR - http://eudml.org/doc/268640
ER -