让$\mathcal{<trans\; data-src="𝒜">𝒜</trans>}$成为首相$<trans\; data-src="\ast ">\ast </trans>$-代数，假设$\mathrm{<trans\; data-src="\Phi ">\Phi </trans>}$保留三倍$<trans\; data-src="\ast ">\ast </trans>$-约旦推导$\mathcal{<trans\; data-src="𝒜">𝒜</trans>}$也就是说，对于每个$\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="B">B</trans>}<trans\; data-src="\in ">\in </trans>\mathcal{<trans\; data-src="𝒜">𝒜</trans>}$,

$$\mathrm{<trans\; data-src="\Phi ">\Phi </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src="◇">◇</trans>\mathrm{<trans\; data-src="B">B</trans>}<trans\; data-src="◇">◇</trans>\mathrm{<trans\; data-src="C">C</trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="\Phi ">\Phi </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src=")">)</trans><trans\; data-src="◇">◇</trans>\mathrm{<trans\; data-src="B">B</trans>}<trans\; data-src="◇">◇</trans>\mathrm{<trans\; data-src="C">C</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src="◇">◇</trans>\mathrm{<trans\; data-src="\Phi ">\Phi </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="B">B</trans>}<trans\; data-src=")">)</trans><trans\; data-src="◇">◇</trans>\mathrm{<trans\; data-src="C">C</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src="◇">◇</trans>\mathrm{<trans\; data-src="B">B</trans>}<trans\; data-src="◇">◇</trans>\mathrm{<trans\; data-src="\Phi ">\Phi </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="C">C</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">,</trans>$$

哪里$\mathrm{<trans\; data-src="A">A类</trans>}<trans\; data-src="◇">◇</trans>\mathrm{<trans\; data-src="B">B</trans>}<trans\; data-src="=">=</trans>\mathrm{<trans\; data-src="A">A类</trans>}\mathrm{<trans\; data-src="B">B</trans>}<trans\; data-src="+">+</trans>\mathrm{<trans\; data-src="B">B</trans>}{\mathrm{<trans\; data-src="A">A类</trans>}}^{<trans\; data-src="\ast ">\ast </trans>}$。那么$\mathrm{<trans\; data-src="\Phi ">\Phi </trans>}$是加性的。此外，如果$\mathrm{<trans\; data-src="\Phi ">\Phi </trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}\mathrm{<trans\; data-src="I">我</trans>}<trans\; data-src=")">)</trans>$是自伴的$\mathrm{<trans\; data-src="\alpha ">\alpha </trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="\{">\{</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">,</trans>\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="\}">\}</trans>$，然后$\mathrm{<trans\; data-src="\Phi ">\Phi </trans>}$是一个$<trans\; data-src="\ast ">\ast </trans>$-推导。