SLIDE 1
▼✐♥✐♠❛❧ ❜♦✉♥❞❛r② ❝♦♥❡s
❈❛✈❛❧❧♦tt♦ ❊❞♦❛r❞♦ ❏❛♥✉❛r② ✶✼✱ ✷✵✶✼
❈❛✈❛❧❧♦tt♦ ❊❞♦❛r❞♦ ▼✐♥✐♠❛❧ ❜♦✉♥❞❛r② ❝♦♥❡s ✶✴✶✽
❆❧♠❣r❡♥ ♠✐♥✐♠✐s❡rs
▲❡t ✉s ✜① ✵ < ❞ < ♥✱ ❊ ✇✐❧❧ ❜❡ ❛ s✉❜s❡t ♦❢ R♥ ✇✐t❤ ❧♦❝❛❧❧② ✜♥✐t❡ ❞✲❞✐♠❡♥s✐♦♥❛❧ ❍❛✉s❞♦r✛ ♠❡❛s✉r❡ H❞✳ ❆❞♠✐ss✐❜❧❡ ❝♦♠♣❡t✐t♦rs ▲❡t ❯ ⊂ R♥ ❜❡ ♦♣❡♥✳ ❋ ✐s ❛♥ ❛❞♠✐ss✐❜❧❡ ❝♦♠♣❡t✐t♦r ❢♦r ❊ ♦♥ ❯ ✐❢ t❤❡r❡ ❡①✐sts ❛ ❝♦♥t✐♥✉♦✉s ❢✉♥❝t✐♦♥ φ : [✵, ✶] × ❯ → ❯ s✉❝❤ t❤❛t✿ φ(✵, ·) = ■❞❀ ∃❑ ⊂⊂ ❯ s✉❝❤ t❤❛t ∀t φ(t, ·) = ■❞ ✐♥ ❑ ❝❀ φ(✶, ·) ✐s ▲✐♣s❝❤✐t③ ❛♥❞ ❋ = φ(✶, ❊)✳ ❲❡ ❝❛❧❧ φ ❛♥ ❛❞♠✐ss✐❜❧❡ ❞❡❢♦r♠❛t✐♦♥✳ ❆❧♠❣r❡♥ ♠✐♥✐♠✐s❡r ❊ ✐s ❛♥ ❆❧♠❣r❡♥ ♠✐♥✐♠✐s❡r ✐❢ ❢♦r ❡✈❡r② ❛❞♠✐ss✐❜❧❡ ❝♦♠♣❡t✐t♦r ❋ ✇❡ ❤❛✈❡✿ H❞(❊ \ ❋) ≤ H❞(❋ \ ❊).
❈❛✈❛❧❧♦tt♦ ❊❞♦❛r❞♦ ▼✐♥✐♠❛❧ ❜♦✉♥❞❛r② ❝♦♥❡s ✷✴✶✽