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 May15 comment length of sum of two submodule @rschwieb: But I only prove the cases $K \cap N =\{0\}$ May15 comment length of sum of two submodule thanks BenjaLim, i will try work on it. But could we prove this without exact sequence concept, instead of directly from definition of composition series? May15 accepted length of sum of two submodule May15 comment length of sum of two submodule How to show that l((K+N)/N)=l(K+N)-l(N)? May15 asked length of sum of two submodule May12 accepted Interpretation of dP in Radon-Nikodym Theorem May12 comment Length of composition series and injective homomorphisms OK, i get it. The composition series of $N$ is the refinement of the series $f(M_0)\subset ... \subset f(M_n)$, so $l(N) \geq n$. May12 accepted Length of composition series and injective homomorphisms May12 comment Length of composition series and injective homomorphisms @user1. I have explain it in my solution. Read carefully before judging! May12 comment Length of composition series and injective homomorphisms With your argument could we conclude that $l(N)=l(M)$? Since every module have the same length of composition series May12 comment Length of composition series and injective homomorphisms @user1: No, Since M isomorphic to Im f and Im f is submodule of N we have $l(M)=l(im f)\leq l(N)$ May12 asked Length of composition series and injective homomorphisms Apr27 asked Interpretation of dP in Radon-Nikodym Theorem Apr15 comment Integral of bivariate normal distribution function with respect to itself Could you prove this using elementary calculus like substitution rule and etc Apr15 asked Integral of bivariate normal distribution function with respect to itself Apr4 revised Independence of $n$ random variables edited body Apr3 comment Independence of $n$ random variables sory, typo bigcup and bigcap Apr3 revised Independence of $n$ random variables edited body Apr3 asked Independence of $n$ random variables Mar27 accepted Finitely generaterd torsion-free module over PID