# Questions tagged [kolmogorov-axioms]

Constitute Kolmogorov's mathematical definition of a probability space. It is a triplet $(\Omega, \mathcal F, P)$ where $P$ has to satisfy three axioms: non-negativity, adding to one, and countable addivity.

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### Definition of recurrent stochastic process, in general

This interesting question: Recurrence definition for a Markov chain gives the definition of a recurrent state for some discrete process. I was wondering, in the case of a continuous (time) process, ...
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### Do uncalibrated "probability" predictions satisfy Kolmogorov's axioms?

Let's say we have some binary variable of interest and fit a model to predict the probability of the two classes, say a logistic regression or a "classification" neural network. This model ...
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### Kolmogorov axioms consequences

Earlier today in my stochastic processes lecture, the prof mentioned that there does not exist a probability measure P(A) defined for all subsets of [0,1] which would satisfy all the 3 Kolmogorov ...
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### Axiomatized formal foundation of statistics

I'm learning statistics in foreign language. Being aware of possibly different foundations (e.g. frequentists v.s. Bayesian), I hope to acquire one formally axiomatized foundation of statistics. That ...
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1 vote
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### Show that if A and B are disjoint, then A ∩ C and B ∩ C are also disjoint

I need to show using Venn diagram. Is my solution correct, I understand from the Venn diagram it would be right, but can someone explain in a more formal/mathematical way why this implication is true? ...
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### How to prove $P(\emptyset)=0$ from the axioms of probability?

A text states that you can prove that a probability of a null set is 0 through one of the axioms of probability. I know the three axioms, but I fail to employ these axioms to prove the above. I ...
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### Explain to my intuition: New axioms for rigorous Bayesian probability

I stumbled upon this very interesting article : New axioms for rigorous Bayesian probability https://projecteuclid.org/euclid.ba/1340369856 Whose aim is to provide new axioms for probability theory ...
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### Can we get uniform distributions on infinite spaces by giving up infinite additivity

I am wondering whether it is possible to translate the idea of drawing a number randomly from the set of all natural numbers. If we have infinite additivity as an axiom this obviously does not work. ...
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