π(π, π) and πΏ(π, π) are upper and lower Riemann sums for the partition p.
U(f,p)=βMiβΞxiβ, L(f,p)=βmiβΞxiβ
Miβ=sup{f(x):xiβ1ββ€xβ€xiβ}, miβ=inf{f(x):xiβ1ββ€xβ€xiβ}
sup{βf(x):xiβ1ββ€xβ€xiβ}=βinf{f(x):xiβ1ββ€xβ€xiβ}=βmiβ
U(βf,p)=ββmiβΞxiβ=βL(f,p)
inf{βf(x):xiβ1ββ€xβ€xiβ}=βsup{f(x):xiβ1ββ€xβ€xiβ}=βMiβ
L(βf,p)=ββMiβΞxiβ=βU(f,p)
Comments
Leave a comment