A monotone isomorphism theorem

In the simple case of a Bernoulli shift on two symbols, zero and one, by permuting the symbols, it is obvious that any two equal entropy shifts are isomorphic. We show that the isomorphism can be realized by a factor that maps a binary sequence to another that is coordinatewise smaller than or equal to the original sequence.Comment: 22 page

Resisting in France and la vie inventée

The daily experience of resistance in occupied France has often been missing from accounts of les années noires. Whether concerned with the deeds of prominent resisters or with the deconstruction of national myths, history has often obscured the experiences of the majority of the significant minority who opted to rebel against oppression. The first two years of the Occupation are often overshadowed by the move towards a unified movement and the increasingly combative stance of the Resistance of the following years. This may be partly related to the difficulty in placing such disparate realities into a coherent methodological framework. Equally, an analysis of events that possessed a surreal and almost dreamlike quality by those that witnessed them may have discouraged attempts to gain a deeper awareness of the phenomenon of resistance. In some respects, it did occupy a different sphere of reality for those that chose not to obey the armistice could be considered marginal in their behaviour and their memory remained so in post-war France as the demands of national reconstruction produced a dominant representation of the period which obscured the experience of the individual. This paper seeks to explore this sub-reality through an analysis of la vie inventée and its manifestation within the creation of an ésprit de résistance, the transmission of this consciousness and the inversion of the hegemony of the Vichy régime. Finally, it will question whether this notion was born from or conversely a prerequisite to La Résistance