Category:Measure Theory Theorems

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Pages in category "Measure Theory Theorems"

The following 39 pages are in this category, out of 39 total.

A

A collection of subsets is a sigma-algebra if and only if it is both a p-system and a d-system
A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections
A function is a measure iff it measures the empty set as 0, disjoint sets add, and it is continuous from below (with equiv. conditions)
A map from two sigma-algebras, A and B, is measurable if and only if for some generator of B (call it G) we have the inverse image of S is in A for every S in G
A pre-measure on a semi-ring may be extended uniquely to a pre-measure on a ring

B

C

D

E

I

Integral of a positive function (measure theory)

M

P

R

Ring generated by

S

T

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