Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
1. Summary
We 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.
CONTENTS
1. Summary..............................................................................................................5
2. Spectral measure theory for Boolean and Heyting algebras................................5
2.1. Introduction.......................................................................................................5
2.2. Spectral measures for Boolean algebras..........................................................5
2.3. Spectral supermeasures for Heyting algebras.................................................11
3. Theory of the integral for Boolean and Heyting algebras...................................14
3.1. Introduction.....................................................................................................14
3.2. Theory of the integral......................................................................................14
4. Some numerical characteristics of random variables on Heyting algebras.........18
4.1. Introduction.....................................................................................................18
4.2. Expectation and variance................................................................................18
4.3. Other fundamental numerical characteristics of random variables..................24
References............................................................................................................28
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
297
Liczba stron
28
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXCVII
Daty
wydano
1990
Twórcy
autor
- ul. Francuska 34 m. 3, 03-905 Warszawa, Poland
Bibliografia
- [1] A. A. Borovkov, A Course in Probability Theory, "Nauka", Moscow 1972 (in Russian).
- [2] G. M. Fikhtengol'ts, Course of Differential nad Integral Calculus, "Nauka", Moscow 1969 (in Russian).
- [3] N. B. Haaser and I. A. Sullivan, Real Analysis, Van Nostrand Reinhold, New York 1971.
- [4] S. Mazurkiewicz, Foundations of Probability, PWN, Warsaw 1956 (in Polish).
- [5] H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, PWN, Warsaw 1968.
- [6] D. E. Rutherford, Introduction to Lattice Theory, Hafner, New York 1965.
- [7] E, Rydzyńska, The conditional probability on Heyting algebras and new geometry of the space of events, J. Math. Phys. Sci. 21(5) (1987).
- [8] E, Rydzyńska, Probability Heyting agebras, Demonstratio Math. 19 (1986), 573-589.
- [9] E, Rydzyńska, Radial hypothesis, Astrophys. and Space Sci. 137 (1987), 183-187.
- [10] R. Sikorski, Advanced Calculus. Functions of Several Variables, PWN, Warsaw 1969.
- [11] V. I. Sobolev, On half-ordered measure of sets, measurable functions and some abstract integrals, Dokl. Akad. Nauk SSSR 91 (1953), 23-26 (in Russian).
- [12] D. A. Vladimirov, Boolesche Algebren, Akademie-Verl., Berlin 1972.
- [13] B. Z. Vulikh, Introduction to the Theory of Half-ordered Fields, Gos. Izd. Fiz.-Mat. Lit., Moscow 1961 (in Russian).
Języki publikacji
| EN |
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-d1406e4a-f257-4385-9972-e8164240f99d
Identyfikatory
ISBN
83-01-09895-3
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.