8. If (X, M, ) is a measure space and {E₁} CM, then (lim inf E₁) ≤ lim inf μ(E). Also, μ(lim sup E₁) ≥ lim sup μ(E;) provided that µ(UE;) < ∞.
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- Suppose that a > 0 is a positive integer, and n > a. How many lattice paths are there from (0, 0) to (n, n) that do not go above the line y = x + a? hint: Catalan Number7) Compute the following limitsIn formally proving that limx→1 (x^2+x)=2, let ε>0 be arbitrary. Chooseδ =min(εm , 1). Determine the smallest value of m that would satisfy the proof.