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6 Nov 2023: Then we define. σ(Xi : i I) = σ ({ω : Xi(ω) B} : i I,B B) ,. i.e. this is the smallest σ-algebra that makes (Xi)iI measurable. 3. ... Moreover, if Y ′ also satisfies (a) and (b), then Y = Y ′ a.s.

22 May 2023: 2s2)/(2s4d)EYf k ef f kH(O) ' c,. where c = c(, s, B, gmin, fmin, d, vol(O)) is a finite positive constant. ... We now prove Proposition 6(B) for (Cc (O)); the case of (CK (O)).

15 Jan 2023: Recall that aCauchy sequence (fm). m=1 in B has ‖fm fn‖B 0 as n,m. ... φ̂ : X Rb. with b small such that E{φ̂(x)Tφ̂(x′)} = k(x,x′).