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Applying two definitions of the union of IF-events, P. Grzegorzewski gave two generalizations of the inclusion-exclusion principle for IF-events.In this paper we prove an inclusion-exclusion principle for IF-states based on a method which can also be used to prove Grzegorzewski's inclusion-exclusion principle for probabilities on IF-events.Finally, we give some applications of this principle by...

The equivalence principle, which states the local equivalence between acceleration and gravity, requires that a free falling observer must result in a co-moving local Minkowski space. On the other hand, covariance principle assumes any Gaussian system to be valid as a space-time coordinate system. Given the mathematical existence of the co-moving local Minkowski space along a time-like geodesic...

Le Chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . However, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. In this article, we derived a simple equation for the violation of...