Translation examples
Mittojen absoluuttinen jatkuvuus on refleksiivinen ja transitiivinen relaatio, mutta se ei ole antisymmetrinen. Siten se on esijärjestys, mutta ei osittainen järjestys.
Absolute continuity of measures is reflexive and transitive, but is not antisymmetric, so it is a preorder rather than a partial order.
Kieltosääntö seuraa siitä, että identtisten fermionien aaltofunktion on oltava antisymmetrinen kahden hiukkasen vaihdossa.
When there are external lines, the amplitudes are antisymmetric when two Fermi insertions for identical particles are interchanged.
Siis: μ ≪ ν ⟺ ( ν ( A ) = 0 ⟹ μ ( A ) = 0 ) . {\displaystyle \mu \ll \nu \iff \left(\nu (A)=0\implies \mu (A)=0\right).} Mittojen absoluuttinen jatkuvuus on refleksiivinen ja transitiivinen relaatio, mutta se ei ole antisymmetrinen.
In symbols: μ ≪ ν ⟺ ∀ A ( ν ( A ) = 0 ⇒ μ ( A ) = 0 ) . {\displaystyle \mu \ll \nu \iff \forall A\left(\nu (A)=0\ \Rightarrow \ \mu (A)=0\right).} Absolute continuity of measures is reflexive and transitive, but is not antisymmetric, so it is a preorder rather than a partial order.
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