  In this monograph, we construct and study a sigma-finite measure on
continuous functions from R_+ to R, strongly related to many probability
measures obtained by penalisation of Brownian motion, i.e. as limits of
probabilities which are absolutely continuous with respect to Wiener measure.
This remarkable sigma-finite measure can be generalized in three other cases:
one can start from a two-dimensional Brownian motion, from a recurrent
diffusion with values in R_+, and from a discrete, recurrent Markov chain.
