Non-commutative geometry – Equivalence of two approaches to transversal measures for a foliation

Suppose that $ (V, F) $ It is a foliated variety. There are three equivalent approaches to the notion of transversal measure as described in this book (see pages 65-69). I would like to understand the last line of section 5.$ alpha $ where it is stated that one easily controls, as in the case of flows, that $ Lambda $ meets definition 2 & # 39; & # 39 ;. So the context is this: one starts with a closed current $ C $ (of degree $ = dim F $) positive in the direction of the sheet and with the help of this current defines a measure $ mu_U $ (locally in $ U $, the domain of the foliation table) in the set of plates by the fromula
$$ langle C, omega rangle = int Big ( int _ { pi} omega Big) d mu_U ( pi). $$
Once we have this measure we can define it. $ Lambda (B): = int Card (B cap pi) d mu_ {U} ( pi) $ for any transverse borel $ B $ (that is, subset of Borel $ B subset V $ such that for each sheet $ L $ of the foliation $ B cap L $ it is at most countable.

Why $ Lambda $ satisfy $ Lambda (B) = Lambda ( psi (B)) $ for any injection of Borel $ psi $ that keeps the leaves.

My guess is that somehow you must follow the condition of $ C $ be closed but I'm not sure how to perform the calculations (for example, one problem I found is that $ Lambda $ It is defined locally and I do not see how to go from $ U $ to another foliation letter $ U & # 39; $ (What can happen by general $ psi $).

measurement theory – Strong convergence of the support operator in spaces $ 0 ^ p $ non-commutative

Leave $ M $ be a von Neumann algebra with a normal faithful semifinite trace $ tau. $ Leave $ L ^ p (M) $be the non-commutative associated $ L ^ p $-space. Suppose, $ x geq 0 $ be an element of $ L ^ p (M) $ Y $ 0 leq x_n leq x $ such that $ x_n $ converges to $ x $ in measure It is true that $ text {support} x_n $ converge to support $ x $ in strong operator topology or weak operator topology or $ sigma $Strong topology?

How to get rid of the brackets that appear in non-commutative multiplication?

I'm getting output as

(-T1T2T3)T4T5

How to get rid of the brackets that appear in the output?

I want my exit as -T1T2T3T4T5

Symbolic non-commutative algebra

Consider 3 noncommutative elements. $ A, B, C $ and we have the relationship $ CB = BC $.

I want to compute things like: $ (A otimes BC) (B otimes B) = AB otimes alpha B ^ 2C $

Is there a package doing this?