A training apparatus comprising: a tight fitting device comprising a band having the length that is enough to be wrapped around a predetermined range of one of the limbs of a user who receives training; an inflatable tube provided in or on said band, said inflatable tube being of air-tight construction; and fastening means for fastening said band on said predetermined range with said band being wrapped around said predetermined range of one of the limbs, said fastening means being provided on said band, said tight fitting device being adapted to apply a predetermined applied pressure to said predetermined range of said limb by means of filling said inflatable tube with a gas, the predetermined applied pressure being for restricting the blood flow into the limb distal to said predetermined range; and measuring means for measuring at least one physical quantity that varies in conjunction with oxygen saturation in said limb on which said tight fitting device is placed, to generate oxygen saturation data associated with an oxygen saturation value that represents the degree of oxygen saturation; the training apparatus being adapted to control said applied pressure; the training apparatus further comprising: pressure regulating means that is capable of forcing a gas into said inflatable tube and removing the gas from said inflatable tube, via a predetermined tube; and control means for controlling said pressure regulating means in order to change said applied pressure; said control means being adapted to receive the oxygen saturation data from said measuring means, and adapted to control said pressure regulating means in such a manner that said pressure regulating means reduces the pressure in said inflatable tube when the oxygen saturation value of the user falls below a reference oxygen saturation value. a tight fitting device comprising a band having the length that is enough to be wrapped around a predetermined range of one of the limbs of a user who receives training; an inflatable tube provided in or on said band, said inflatable tube being of air-tight construction; and fastening means for fastening said band on said predetermined range with said band being wrapped around said predetermined range of one of the limbs, said fastening means being provided on said band, said tight fitting device being adapted to apply a predetermined applied pressure to said predetermined range of said limb by means of filling said inflatable tube with a gas, the predetermined applied pressure being for restricting the blood flow into the limb distal to said predetermined range; and measuring means for measuring at least one physical quantity that varies in conjunction with oxygen saturation in said limb on which said tight fitting device is placed, to generate oxygen saturation data associated with an oxygen saturation value that represents the degree of oxygen saturation; the training apparatus being adapted to control said applied pressure; the training apparatus further comprising: pressure regulating means that is capable of forcing a gas into said inflatable tube and removing the gas from said inflatable tube, via a predetermined tube; and control means for controlling said pressure regulating means in order to change said applied pressure; said control means being adapted to receive the oxygen saturation data from said measuring means, and adapted to control said pressure regulating means in such a manner that said pressure regulating means reduces the pressure in said inflatable tube when the oxygen saturation value of the user falls below a reference oxygen saturation value. pressure regulating means that is capable of forcing a gas into said inflatable tube and removing the gas from said inflatable tube, via a predetermined tube; and control means for controlling said pressure regulating means in order to change said applied pressure; said control means being adapted to receive the oxygen saturation data from said measuring means, and adapted to control said pressure regulating means in such a manner that said pressure regulating means reduces the pressure in said inflatable tube when the oxygen saturation value of the user falls below a reference oxygen saturation value.