On Dahlberg’s Lusin area integral theorem

A Quantitative Lusin Theorem for Functions in BV

We extend to the BV case a measure theoretic lemma previously proved by DiBenedetto, Gianazza and Vespri ([1]) in W 1,1 loc . It states that if the set where u is positive occupies a sizable portion of a open set E then the set where u is positive clusters about at least one point of E. In this note we follow the proof given in the Appendix of [3] so we are able to use only a 1−dimensional Poin...

A constructive version of the Lusin Separation Theorem

A Saitô–tomita–lusin Theorem for Jb∗-triples and Applications

A theorem of Lusin is proved in the non-ordered context of JB∗-triples. This is applied to obtain versions of a general transitivity theorem and to deduce refinements of facial structure in closed unit ballls of JB∗-triples and duals.

On a Theorem of Banach and Kuratowski and K-lusin Sets

In a paper of 1929, Banach and Kuratowski proved—assuming the continuum hypothesis—a combinatorial theorem which implies that there is no nonvanishing σ-additive finite measure μ on R which is defined for every set of reals. It will be shown that the combinatorial theorem is equivalent to the existence of a K-Lusin set of size 20 and that the existence of such sets is independent of ZFC + ¬CH.

Cauchy Integral Theorem

where we use the notation dxI for (1.4) dxI = dxi1 ∧ dxi2 ∧ ... ∧ dxik for I = {i1, i2, ..., ik} with i1 < i2 < ... < ik. So ΩX is a free module over C ∞(X) generated by dxI . Obviously, Ω k X = 0 for k > n and ⊕ΩX is a graded ring (noncommutative without multiplicative identity) with multiplication defined by the wedge product (1.5) ∧ : (ω1, ω2)→ ω1 ∧ ω2. Note that (1.6) ω1 ∧ ω2 = (−1)12ω2 ∧ ω...