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Abstract. In this article we expose a proof of the Canonical Decomposi- tion Theorem of irreducible 3-manifolds along tori and annuli, also known as JSJ Theorem. This proof will
The proof of the following theorem known till now is based on the martingale theory (see e.g. We give a \pure dyadic analysis" proof for it.. Theorem 5. [AVD]), then can be
Lemma 7. The first statement is trivial.. In the following Theorem we include it for sake of completeness... Theorem 9.. We also use the well-known properties of the Lambert
The proof of May's uniqueness theorem (Ma4] Thm. 3) for functors dened from the category of permutative categories easily generalizes to show any two functors from SymMon to
So we shall prove the following theorem which as a particular case contains the answer to the problem..
To prove this, we use the same idea as in the proof of the theorem of Bichteler–Dellacherie–Mokobodzki which consists in the following: the continuity of the functional J and
The proof of Lemma 9 is based on the well-known Besicovitch theorem on possible values of upper and lower derivative numbers (see [1], Ch.IV,.. § 3) and is carried out analogously
The Radon Nikodym Theorem plays a key role in our proof of the Fundamen- tal Theorem of Calculus, particularly the proof given by Bradley [4], so we will outline this proof but
