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https://math.stackexchange.com/questions/40882/mutually-singular-measures-with-the-same-support
To be more challenging, let's find an uncountable family of mutually singular finite measures all of which have the unit interval as its support and give measure zero to countable subsets. This sort of family is actually something that occurs naturally in ergodic theory if you know ergodic decomposition.
https://math.stackexchange.com/questions/40975/support-of-a-measure
The support of a measure should be the smallest set outside of which a measure always vanishes. Now a point measure is obviously supported at that point, while Lebesgue measure has full support and you could always pick a point measure inside the "support" of the Lebesgue measure.
https://en.wikipedia.org/wiki/Support_(mathematics)
Singular support In Fourier analysis in particular, it is interesting to study the singular support of a distribution. This has the intuitive interpretation as the set of …
https://math.berkeley.edu/~mpejic/pdfdocuments/SingularContinuousMeasures.pdf
If (X) is nite, is termed a nite measure; if X can be expressed as the countable union of sets in A, each of which has nite measure, then is termed a ˙- nite measure. The support of a measure is the largest closed set such that any open subset of it has nonzero measure. A function f: X![1 ;1] is A-measurable if the preimage f 1 ((c;1]) is in Afor all
https://www.encyclopediaofmath.org/index.php/Singular_measures
Singular measures. 2010 Mathematics Subject Classification: Primary: 28A15 [ MSN ][ ZBL ] If μ and ν are two σ -finite measures on the same σ-algebra B of subsets of X, then μ and ν are said to be singular (or also mutually singular…
https://en.wikipedia.org/wiki/Singular_measure
Singular measure. In mathematics, two positive (or signed or complex) measures μ and ν defined on a measurable space (ω, σ) are called singular if there exist two disjoint sets A and B in σ whose union is ω such that μ is zero on all measurable subsets of B while ν is zero on all measurable subsets of A. This is denoted by μ ⊥ ν .
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https://dictionary.cambridge.org/us/dictionary/english/singular
singular meaning: 1. of or relating to the form of a word used when talking or writing about one thing: 2. of an…. Learn more.
https://www.wordhippo.com/what-is/the-plural-of/measure.html
The plural form of measure is measures. Find more words! Another word for Opposite of Meaning of Rhymes with Sentences with Find word forms Translate from English Translate to English Words With Friends Scrabble Crossword / Codeword Words starting with Words ending with Words containing exactly Words containing letters Pronounce Find ...
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