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valsi 
ma'au 
type 
experimental cmavo 
creator 
krtisfranks 
time entered 
Mon Apr 2 17:12:13 2018 
Examples


English


Definition #70586
 Preferred
[edit]


selma'o 
VUhU 
definition 
Binary mekso operator: uniform probability
A(X_{2})u(X_{1}, X_{2}) for input (X_{1}, X_{2}) where X_{1} is a number and X_{2} is a set or space. (See notes for details).

notes 
Establish (elsewhere) a universal set/topological space O and equip it with a measure L; then X_{1} must be anĀ element of O, and X_{2} must be a subset/subspace of O and will be equipped with/inherit the same measure L (restricted to it) and the appropriate topology. Let Y be the maximal nondiscrete subset/subspace of X_{2} (in other words, all nondiscrete subsets/subspaces of X_{2} are subsets/subspaces of Y). The term 'A' in the definition is a nonnegativevalued 'function' which is defined on the category of sets; it produces the proper normalization (by being the reciprocal of the integral of u over O with respect to L iff such is welldefined and finite and positive; otherwise, it is identically 0). The term 'u' in the definition is defined to be the sum of the indicator function (Kronecker delta) for Y (outputting 1 iff X_{1} is an element Y, and outputting 0 otherwise) and the Dirac delta of: 1 minus the indicator function for the relative complement of Y in X_{2} (id est: X_{2}
Y); it should be noted that all functions mentioned are defined on all of O but have nonzero values according to only the previous description (in particular, u = 0 identically in O
X_{2}); the indicator functions directly are functions of the input X_{1}. See also: "zdeltakronekre", "zdeltadirake".

gloss words 

created by 
krtisfranks 
vote information 
1

time 
Mon Apr 2 17:14:15 2018 



Examples




