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On mean value in $F$-quantum spaces
Applications of Mathematics, Tome 35 (1990) no. 3, pp. 209-214
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The paper deals with a new mathematical model for quantum mechanics based on the fuzzy set theory [1]. The indefinite integral of observables is defined and some basic properties of the integral are examined.
The paper deals with a new mathematical model for quantum mechanics based on the fuzzy set theory [1]. The indefinite integral of observables is defined and some basic properties of the integral are examined.
DOI : 10.21136/AM.1990.104404
Classification : 03E72, 03G12, 04A72, 60A99, 81C20, 81P10
Keywords: quantum mechanics; observables; states; probability; fuzzy sets; $F$-quantum space; indefinite integral of observables 
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Riečan, Beloslav. On mean value in $F$-quantum spaces. Applications of Mathematics, Tome 35 (1990) no. 3, pp. 209-214. doi: 10.21136/AM.1990.104404

[1] B. Riečan: A new approach to some notions of statistical quantum mechanics. Busefal 36, 1988, 4-6.

[2] B. Riečan A. Dvurečenskij: On randomness and fuzziness. In: Progress in Fuzzy Sets in Europe, (Warszawa 1986), PAN, Warszawa 1988, 321-327.

[3] A. Dvurečenskij B. Riečan: On joint distribution of observables for F-quantum spaces. Fuzzy Sets and Systems. | MR

[4] A. Dvurečenskij B. Riečan: Fuzziness and commensurability. Fasciculi Mathematici.

[5] A. Dvurečenskij F. Chovanec: Fuzzy quantum spaces and compatibility. Int. J. Theor. Phys. 27 (1988), 1069-1082. | DOI | MR

[6] A. Tirpáková: On a sum of observables in F-quantum spaces and its applications to convergence theorems. In: Proc. of the First Winter School on Measure Theory (Liptovský Ján 1988), 68-76.

[7] A. Dvurečenskij A. Tirpáková: A note on a sum of observables in F-quantum spaces and its properties. Busefal 36 (1988), 132-137.

[8] A. Dvurečenskij A. Tirpáková: Sum of observables in fuzzy quantum soaces and convergence theorems.

[9] K. Piasecki: On the extension of fuzzy P-measure generated by outer measure. In: Proc. 2nd Napoli Meeting on the Mathematics of Fuzzy Systems 1985, 119-135.

[10] A. Dvurečenskij: The Radon-Nikodým theorem for fuzzy probability spaces.

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