Markovianity and the Thompson monoid F+

We introduce a new distributional invariance principle, called ‘partial spreadability’, which emerges from the representation theory of Thompson monoid F+ in noncommutative probability spaces. show that partially spreadable sequence random variables is adapted to local Markov filtration. Conversely we large class stationary sequences provides representations F+. In particular case classical space, arrive at de Finetti theorem for with values standard Borel space.