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Today I was reading in a probabilities textbook that the probability of the union of two events is:

[TEX] p(E_1 \cup E_2) = p(E_1) + p(E_2) - p(E_1 \cap E_2) [/TEX]

and reminded me of the similarity with the dimension of the union of two subspaces of a vector space:

[TEX] dim(V_1 \cup V_2) = dim(V_1) + dim(V_2) - dim(V_1 \cap V_2) [/TEX]

Question is: is there a theory/generalization that makes two concepts a particular case of this more general theory? (they look very similar so there must be something common with those concepts)

Thanks,

Damián.

[TEX] p(E_1 \cup E_2) = p(E_1) + p(E_2) - p(E_1 \cap E_2) [/TEX]

and reminded me of the similarity with the dimension of the union of two subspaces of a vector space:

[TEX] dim(V_1 \cup V_2) = dim(V_1) + dim(V_2) - dim(V_1 \cap V_2) [/TEX]

Question is: is there a theory/generalization that makes two concepts a particular case of this more general theory? (they look very similar so there must be something common with those concepts)

Thanks,

Damián.

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