  A universally valid uncertainty relation proposed by Ozawa is re-investigated
under for the generalized equation of motion with some boundary condition.
Necessary conditions for violation (lessening) of the Heisenberg-type
uncertainty relation is discussed in detail. An experimental test of lessening
of the generalized uncertainty relation due to the boundary condition is shown
by re-analyzing the data measuring electron densities of hydrogen molecule
encapsulated in a cage of fullerene C60.
