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IJMMS
TRANSLATION INVARIANCE AND FINITE ADDITIVITY IN A PROBABILITY MEASURE ON THE NATURAL NUMBERS
**ROBERT** **GARDNER**
ROBERT PRICE
Inspired by the ?two envelopes exchange paradox,? a finitely additive ... propose that, in the
setting of the two envelopes problem, probabilities and expected values be computed
as above.
**Robert** **Gardner**: Department of Mathematics, Box 70663, East Tennessee State
University

IJMMS
TRANSLATION INVARIANCE AND FINITE ADDITIVITY IN A PROBABILITY MEASURE ON THE NATURAL NUMBERS
**ROBERT** **GARDNER**
ROBERT PRICE
Inspired by the ?two envelopes exchange paradox,? a finitely additive ... propose that, in the
setting of the two envelopes problem, probabilities and expected values be computed
as above.
**Robert** **Gardner**: Department of Mathematics, Box 70663, East Tennessee State
University

IJMMS
TRANSLATION INVARIANCE AND FINITE ADDITIVITY IN A PROBABILITY MEASURE ON THE NATURAL NUMBERS
**ROBERT** **GARDNER**
ROBERT PRICE
Inspired by the “two envelopes exchange paradox,” a finitely additive ... propose that, in the
setting of the two envelopes problem, probabilities and expected values be computed
as above.
**Robert** **Gardner**: Department of Mathematics, Box 70663, East Tennessee State
University

We propose a quantum generalisation of a classical neural network. The classical neurons are firstly rendered reversible by adding ancillary bits. Then they are generalised to being quantum reversible, i.e., unitary (the classical networks we generalise are called feedforward, and have step-function activation functions). The quantum network can be trained efficiently using...