Yesterday I was all day working on commutative diagrams to make a connection between g and f. My guess was either g is marginalization of f or g is conditioning of f or something between it. It turns out that g is induced measure of f that is g corresponds to conditional probability provided the...
I agree that's the standard way to approach probability theory. I was however interested in some weaker form of probablity theory. Thanks again for the quick response.
Thanks for the quick reply. Yes it is a kind of measure. Let me further clarify my problem. Let T be a topology on X. Now assign real values to each open set of X by f:T->R. Next I remove the whole neighborhood system (N_x) of a prticular point x from T, i.e. T\N_x. Next I have shown that T\N_x...
Let (X, τ) be a topolgical space. Let f: τ→R be a map that assigns real values to the elements of τ. Let (A,τ_A) be subspace of (X,τ). Let g:τ_A→R be another map that assigns real values to the element of subspace topology. My question is how the function g is related with function f given that...