Bounded filtered-complex convergence theorem
= Bounded filtered-complex convergence theorem
{title2=$E_1^{p,q}=H^{p+q}(F^pC/F^{p+1}C)\Rightarrow H^{p+q}(C)$}
A finite filtration of a <cochain complex> produces a convergent <spectral sequence>. The induced abutment filtration is the image of $H^n(F^pC)\to H^n(C)$. Finiteness in each degree suffices; a bounded range of cochain degrees is not required.