Definition of basis noun in Oxford Advanced American Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
The only explanation I've ever seen is that a set is measurable if it 'breaks up' other sets in the way you'd want. I don't really see why this is the motivation though. One reason I am not comfortable with it is that you require a measurable set to break up sets which, according to this definition, are non-measurable; why would you require that?
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: the bottom of something considered as its foundation. Fruit juice constitutes the basis of jelly. He is on a first-name basis with his customers.
BASIS definition: the bottom or base of anything; the part on which something stands or rests. See examples of basis used in a sentence.
BASIS meaning: 1. the most important facts, ideas, etc. from which something is developed: 2. a way or method of…. Learn more.
a basic fact, amount, standard, etc., used in making computations, reaching conclusions, or the like: The nurse is paid on an hourly basis. He was chosen on the basis of his college grades.
(topology) A collection of subsets ("basis elements") of a set, such that this collection covers the set, and for any two basis elements which both contain an element of the set, there is a third basis element contained in the intersection of the first two, which also contains that element.