It is said by H. Hardy : "Many of the difficulties of measure theory and all the pathology of the subject arise from the existence of sets of measure zero. The algebraic treatment gets rid of this source of unpleasantness by refusing to consider sets at all; it considers sets modulo sets of measure zero instead."

Also G. C. Rota : "Among probabilists, mention of sample points in an argument has always been bad form. A fully probabilistic argument must be pointless."

I have made some researches in order to find some consistent examples relative to the justifications of these assertions but I didn't find anything more essential.

I know that the events are not pertaining to quantum mechanics because quantum probability is a pointless probability. Morevever, we can model events by orthogonal projectors on a Hilbert Space $\mathcal{H}$, and by taking a commutative von Neumann algebra $\mathcal{M}$ together with a normal state on it as the fundamental system from which everything can be derived, as opposed to Kolmogorov's axiomatisation of classical probability theory. In the noncommutative probability theory, the pair $(\mathcal{A}, \tau)$ is termed a noncommutative probability space. It is here natural to see that kind of probability doesn't include points.

I look for concrete examples which are inadequate for probabilistic reasoning.

It is said by Halmos, P.R.; in "Lectures on ergodic theory" "Many of the difficulties of measure theory and all the pathology of the subject arise from the existence of sets of measure zero. The algebraic treatment gets rid of this source of unpleasantness by refusing to consider sets at all; it considers sets modulo sets of measure zero instead."

Also G. C. Rota in : Twelve problems in probability no one likes to bring up, in Algebraic Combinatorics and Computer Science : a tribute to Gian-Carlo Rota, Henry Crapo and Domenico Senato (eds.), Springer{Verlag, Milano, 2001, pp. 57{93, (1956), Math. Soc. Japan:

"Among probabilists, mention of sample points in an argument has always been bad form. A fully probabilistic argument must be pointless."

I have made some researches in order to find some consistent examples relative to the justifications of these assertions but I didn't find anything more essential.

I know that the events are not pertaining to quantum mechanics because quantum probability is a pointless probability. Morevever, we can model events by orthogonal projectors on a Hilbert Space $\mathcal{H}$, and by taking a commutative von Neumann algebra $\mathcal{M}$ together with a normal state on it as the fundamental system from which everything can be derived, as opposed to Kolmogorov's axiomatisation of classical probability theory. In the noncommutative probability theory, the pair $(\mathcal{A}, \tau)$ is termed a noncommutative probability space. It is here natural to see that kind of probability doesn't include points.

I look for concrete examples which are inadequate for probabilistic reasoning.

It is said by H. Hardy : "Many of the difficulties of measure theory and all the pathology of the subject arise from the existence of sets of measure zero. The algebraic treatment gets rid of this source of unpleasantness by refusing to consider sets at all; it considers sets modulo sets of measure zero instead."

Also G. C. Rota : "Among probabilists, mention of sample points in an argument has always been bad form. A fully probabilistic argument must be pointless."

I have made some researchs in order to find some consistent examples relative to the justifications of these assertions but I din't find nothing more essential.

I know that the events are not pertaining to quantum mechanics because quantum probability is a pointless probability. Morevever, we can modeled events by orthogonal projectors on a Hilbert Space $\mathcal{H}$, and taking a commutative von Neumann algebra $\mathcal{M}$ together with a normal state on it as the foundamental system from which every thing can be derived, as opposed to Kolmogorov's axiomatisation of classical probability theory. In the noncommutative probability theory, the paire $(\mathcal{A}, \tau)$ is termed a noncommutative probability space. It is here naturel to see that kind of probability doesn't include point.

I look for concret examples which are inedequates to probabilistic reasonnings.

It is said by H. Hardy : "Many of the difficulties of measure theory and all the pathology of the subject arise from the existence of sets of measure zero. The algebraic treatment gets rid of this source of unpleasantness by refusing to consider sets at all; it considers sets modulo sets of measure zero instead."

Also G. C. Rota : "Among probabilists, mention of sample points in an argument has always been bad form. A fully probabilistic argument must be pointless."

I have made some researches in order to find some consistent examples relative to the justifications of these assertions but I didn't find anything more essential.

I know that the events are not pertaining to quantum mechanics because quantum probability is a pointless probability. Morevever, we can model events by orthogonal projectors on a Hilbert Space $\mathcal{H}$, and by taking a commutative von Neumann algebra $\mathcal{M}$ together with a normal state on it as the fundamental system from which everything can be derived, as opposed to Kolmogorov's axiomatisation of classical probability theory. In the noncommutative probability theory, the pair $(\mathcal{A}, \tau)$ is termed a noncommutative probability space. It is here natural to see that kind of probability doesn't include points.

I look for concrete examples which are inadequate for probabilistic reasoning.